front.math.ucdavis.edu, MathSciNet, and mail.google.com to the sites supported by default, and added miscellaneous characters and TeX commands missing in the original script.

http://front.math.ucdavis.edu/""> http://front.math.ucdavis.edu/ http://front.math.ucdavis.edu/0001.5063"" rel=""nofollow"">this paper by Kruskal-Quinn.

http://front.math.ucdavis.edu/0001.5132"">here. (I should mention that http://front.math.ucdavis.edu/0002.5222"" rel=""nofollow""> http://front.math.ucdavis.edu/0002.5222 for the explicit relation between representations constructed via hypergeometric integrals and Gassner. We also explain the connection to [DM]. The representations we construct in the paper are mildly different from the ones in [DM], but you just have to replace our parameters $\epsilon_j=\pm 1$ with $\sqrt{-1}$ (to get [DM]).

http://front.math.ucdavis.edu/0004.5147"" rel=""nofollow""> here.

http://front.math.ucdavis.edu/0005.4732"" rel=""noreferrer"">See here for example for a completely elementary proof of it.

http://front.math.ucdavis.edu/0005.5105"" rel=""nofollow noreferrer"">this paper).

http://front.math.ucdavis.edu/0005.5139"" rel=""nofollow noreferrer"">paper ""Rational points near curves and small nonzero $|x^3-y^2|$ via lattice"" by Noam Elkies It was discussed in a previous MO question.

http://front.math.ucdavis.edu/0005.5252"">here which avoid asymptotic cones (in the case you do not accept the Axiom of Choice).

http://front.math.ucdavis.edu/0005.5289"" rel=""nofollow""> Optimistic calculations about the Witten--Reshetikhin--Turaev invariants of closed three-manifolds obtained from the figure-eight knot by integral Dehn surgeries. Hitoshi Murakami. Surikaisekikenkyusho Kokyuroku No. 1172, (2000), 70--79.
http://front.math.ucdavis.edu/0006.5137"" rel=""noreferrer"">here (thanks to LK for ref), some call it ""sphericalization"". http://front.math.ucdavis.edu/0006.5192"">these papers, which extract an invariant from the theta-divisor of the Heegaard surface, appear to have been based on thinking about what happens to the Seiberg-Witten equations when one has a neck Sx[-T,T] (S is the Heegaard surface) with the metric on S at t=-T itself having long cylinders over the compressing circles for one handlebody, while the metric on S at t=T has long cylinders over the compressing circles for the other handlebody.

http://front.math.ucdavis.edu/0007.5165"" rel=""noreferrer"">paper. This is similar to the previous paper of theirs that I cite, but terser and for K-theory.

http://front.math.ucdavis.edu/0008.5185"" rel=""noreferrer"">by Susumu Hirose using a complex of non-separating curves.
http://front.math.ucdavis.edu/0009.5053"" rel=""nofollow"">Flops and Derived Categories he constructs certain derived equivalences (which are Fourier-Mukai transforms so have a Morita type flavour) by building a moduli space for certain objects in a derived category which come from a t-structure.

http://front.math.ucdavis.edu/0010.5032"" rel=""noreferrer"">More on vanishing cycles and mutation, sets $k = \mathbf{Z}/2\mathbf{Z}$.

http://front.math.ucdavis.edu/0010.5223""> another paper of Yagasaki.

http://front.math.ucdavis.edu/0010.5223""> this paper.

http://front.math.ucdavis.edu/0010.5224"" rel=""nofollow"">this paper by Yagasaki, http://front.math.ucdavis.edu/0012.5021""> http://front.math.ucdavis.edu/0012.5021 . As in David Roberts's comment, I think one can also do the same for triangulated categories that arise from stable $(\infty,1)$-categories.

http://front.math.ucdavis.edu/0101.5168"" rel=""noreferrer"">Noam Elkies.

http://front.math.ucdavis.edu/0102.5154"">Manning's paper).

http://front.math.ucdavis.edu/0103.5234"" rel=""nofollow"">Kiran Kedlaya's paper on constructing $A_n$ extensions of $\mathbb{Q}$ with specified discriminant, and following the references there in. The main point of the paper is to construct polynomials with squarefree discriminant, subject to various conditions.

http://front.math.ucdavis.edu/0105.5225"" rel=""noreferrer"">Quantization of Slodowy slices. The trick is this: let $e$ be your fixed nilpotent, by Jacobson-Morozov, we can choose $f,h$ that satisfy the relations of $\mathfrak{sl}_2$ (you need to do this to define the Slodowy slice anyways). In particular, $e$ has $h$-weight 2 under the adjoint action. Furthermore, the subspace $\mathrm{ker}(f)$ is invariant under $h$ (since $[h,f]=-2f$). Thus, if we let $H(t)=\mathrm{exp}(h\log t)$, then $H(t)\cdot e=t^2 e$, so the square of scalar multiplication times $H(t^{-1})$ preserves $e$, that is $t^2H(t^{-1})\cdot e=e$. Since $\mathrm{ker}(f)$ is invariant under both these actions, we have that $e+\mathrm{ker}(f)$, the Slodowy slice is invariant as well.

http://front.math.ucdavis.edu/0105.5225"">Gan and Ginzburg).

http://front.math.ucdavis.edu/0106.5063"" rel=""nofollow""> http://front.math.ucdavis.edu/0106.5063

http://front.math.ucdavis.edu/0107.4705"" rel=""nofollow"">arXiv:math-ph/0107005 by Brydges and Imbrie two approaches for proving this result arise:

http://front.math.ucdavis.edu/0107.5011"" rel=""nofollow"">The honeycomb model of GL(n) tensor products II: Puzzles determine facets of the Littlewood-Richardson cone"" by Allen Knutson and Terry Tao.

http://front.math.ucdavis.edu/0107.5011"">known. All known descriptions of it involve combinatorics, and I daresay that will continue.

http://front.math.ucdavis.edu/0107.5031"" rel=""nofollow""> http://front.math.ucdavis.edu/0107.5031

http://front.math.ucdavis.edu/0108.5038"">this paper studies a two-parameter version.

http://front.math.ucdavis.edu/0109.5170"" rel=""nofollow noreferrer"">appear to have studied obstruction theory in more general settings, it's not clear to me how to squeeze out the appropriate concrete computational gadgets (e.g., the cohomology groups $H^n(X; \pi_{n - 1}(Y))$) from the relevant abstract nonsense. Of course, if somebody could elucidate how that works, that would be wonderful, although perhaps that should be the subject of another question...

http://front.math.ucdavis.edu/0110.5043"" rel=""nofollow"">On families of triangular Hopf algebras by Etingof and Gelaki that this Hopf algebra will be a twist of the original one, and thus $F$ induces a twisted automorphism of $H$. Conversely, any twisted automorphism of $F$ gives rise to an autoequivalence of $G\operatorname{-Mod}$. Natural transformations of monoidal functors correspond to gauge equivalences of twisted automorphisms. Thus, we can identify isomorphism classes of monoidal autoequivalences of $G-\operatorname{Mod}$ with gauge equivalence classes of twisted automorphisms of $k[G]$.

http://front.math.ucdavis.edu/0110.5101"" rel=""nofollow"">work on formalizing the notion of a ""homotopy algebra"" (over a given Lawvere theory). The idea seems to be that an algebra over a Lawvere theory is something you can make homotopyish without recourse to things like operads: given $T$, a homotopy $T$-algebra is a functor $T \to \mathrm{Spaces}$ which preserves products up to homotopy equivalence (rather than on the nose).

http://front.math.ucdavis.edu/0111.5043"" rel=""nofollow noreferrer"">arXiv preprint). But there is a detail in section 6.2 case (c) and case (d) that I do not follow, and would be very grateful, if anyone could clarify it.

http://front.math.ucdavis.edu/0111.5090"" rel=""nofollow"">here.

http://front.math.ucdavis.edu/0111.5139"">Module categories, weak Hopf algebras and modular invariants. However, the basic definition of module category makes perfect sense in general, so I am wondering if there has been any work done in more general settings.

http://front.math.ucdavis.edu/0112.5150"" rel=""noreferrer"">paper on the equivariant cohomology of the Grassmannian

http://front.math.ucdavis.edu/0201.5176"" rel=""nofollow"">haines-pettit and D-module structure of R[F]-modules and

http://front.math.ucdavis.edu/0201.5207"" rel=""noreferrer""> http://front.math.ucdavis.edu/0201.5207 for a generalization of this example).

http://front.math.ucdavis.edu/0202.5286"">nice survey.

http://front.math.ucdavis.edu/0203.5047"" rel=""noreferrer"">Feehan and Leness used to work hard on this, and some of their partial progress was used e.g. in the work of Kronheimer-Mrowka resolving Property (P).

http://front.math.ucdavis.edu/0203.5096"" rel=""nofollow"">Hausel and Sturmfels and http://front.math.ucdavis.edu/0203.5139"" rel=""nofollow noreferrer"">survey http://front.math.ucdavis.edu/0203.5139.

http://front.math.ucdavis.edu/0203.5262"" rel=""nofollow noreferrer"">Benjamini, Kalai and Schramm. There's a newer paper by Benaïm and Rossignol, which I haven't read. I guess that most of the results apply to this setting as well.

http://front.math.ucdavis.edu/0203.5262"" rel=""nofollow noreferrer"">First Passage Percolation Has Sublinear Distance Variance

http://front.math.ucdavis.edu/0204.5007""> http://front.math.ucdavis.edu/0204.5007), which contains a beautiful construction that achieves $f(P)>5.048$, and shows that it is not bounded for strongly regular CW decompositions of the 3-sphere (instead of polytopes). I don't know whether there has been more recent progress.

http://front.math.ucdavis.edu/0204.5218"" rel=""nofollow"">Bondal and van den Bergh give a proof here that $D^b(\mathrm{Coh}X)$ is saturated which is a strong representability condition on cohomological/homological functors to the category of $k$ vector spaces. It follows immediately that $D^b(\mathrm{Coh}X)$ has a Serre functor by using the fact that $Hom(A,-)^*$ is representable for every bounded complex of coherent sheaves $A$.

http://front.math.ucdavis.edu/0204.5275"" rel=""nofollow"">here. Your set-up is essentially equivalent to studying the same problem for a semisimple algebraic group and its Lie algebra in arbitrary chaeracteristic, but good characteristic (including 0) is essential for getting uniform results.

http://front.math.ucdavis.edu/0204.5275"" rel=""nofollow"">here.

http://front.math.ucdavis.edu/0205.5048"" rel=""nofollow noreferrer"">link to the corrected arXiv version of Baohua Fu's 2003 Invent. Math. paper Symplectic resolutions for nilpotent orbits.

http://front.math.ucdavis.edu/0205.5057"">counting components of normal curves.

http://front.math.ucdavis.edu/0205.5144"" rel=""nofollow noreferrer"">here.)

http://front.math.ucdavis.edu/0205.5186"" rel=""nofollow"">here). This involves tilting modules and their Frobenius twists.

http://front.math.ucdavis.edu/0206.5244"" rel=""nofollow""> http://front.math.ucdavis.edu/0206.5244"" rel=""nofollow"">BEV05

http://front.math.ucdavis.edu/0206.5244""> http://front.math.ucdavis.edu/0206.5244 by Bravo, Encinas and Villamayor which has a lot more discussion (it's about 100 pages instead of about 30).

http://front.math.ucdavis.edu/0206.5244

http://front.math.ucdavis.edu/0208.5039"" rel=""nofollow"">theorem of Kuperberg, a virtual knot corresponds http://front.math.ucdavis.edu/0208.5107v2"" rel=""nofollow noreferrer"">the best (least decategorified) proof I've seen. He takes three Schubert cycles meeting transversely, and for each point of intersection, constructs an actual invariant vector inside the corresponding triple product of representations. The set of such vectors is then a basis. http://front.math.ucdavis.edu/0208.5228"" rel=""nofollow"">Choosing roots of polynomials smoothly, II, math.CA/0208228

http://front.math.ucdavis.edu/0209.5053"" rel=""nofollow noreferrer"">here work exclusively over $\mathbb{C}$. Their main theorem shows that (for $G$ http://front.math.ucdavis.edu/0209.5078"" rel=""nofollow"">The Kadison-Singer problem in discrepancy theory for a combinatorial reformulation in terms of finite sets of vectors in ${\bf C}^n$.

http://front.math.ucdavis.edu/0209.5165"" rel=""nofollow"">Thomas Schick.

http://front.math.ucdavis.edu/0209.5199"" rel=""nofollow noreferrer"">survey on Gorenstein rings. You can pick up a lot about them from there, including the very interesting history. To quote from the Introduction:

http://front.math.ucdavis.edu/0209.5256"" rel=""nofollow"">have a paper on that topic.

http://front.math.ucdavis.edu/0209.5256"">this paper.)

http://front.math.ucdavis.edu/0210.5087"" rel=""noreferrer""> http://front.math.ucdavis.edu/0210.5087 )

http://front.math.ucdavis.edu/0210.5482"" rel=""nofollow"">implemented by Fenley to find laminar-free 3-manifolds, and in principle could be used to prove that a 3-manifold is non-Haken. However, it seems that this requires an exponential search.

http://front.math.ucdavis.edu/0211.5159"">his first paper). There are several unresolved issues having to do with the formation of the singularities in Ricci flow that make this question difficult. On the other hand, recently Angenent, Knopf, and Caputo have shown that one may do a canonical surgery in the rotationally symmetric case: Minimally invasive surgery for Ricci flow singularities. There are several simplifications in the rotationally symmetric case http://front.math.ucdavis.edu/0301.5140"" rel=""nofollow"">paper for some more details. http://front.math.ucdavis.edu/0301.5208"" rel=""noreferrer"">survey.

http://front.math.ucdavis.edu/0301.5285"">arXiv:0301.5285.

http://front.math.ucdavis.edu/0302.5208"" rel=""nofollow"">Minsky's work on a priori bounds for surface groups, which is used in the proof of the ending lamination conjecture. http://front.math.ucdavis.edu/0303.5109"" rel=""noreferrer"">Perelman). A fortiori, he proves that any 3-manifold with positive scalar curvature is of this form (and therefore contains a conformally flat positive scalar curvature metric).

http://front.math.ucdavis.edu/0303.5173"" rel=""noreferrer""> http://front.math.ucdavis.edu/0303.5173), Frenkel and Gaitsgory give a new proof of part (2) above. Their idea is to factor $ \Gamma : D^\lambda_{G/B}-mod \rightarrow U\mathfrak g - mod $ in two steps: http://front.math.ucdavis.edu/0303.5249"">Martelli and Petronio. The point is that you can get a triangulation of a $(p,q)$ torus knot with the number of tetrahedra growing like the continued fraction expansion of $p/q$, which can be like $log(|p|+|q|)$, but the genus is $(p-1)(q-1)/2$.

http://front.math.ucdavis.edu/0304.5058"" rel=""nofollow"">Ben Green and Alexander Sapozhenko.

http://front.math.ucdavis.edu/0305.5049"" rel=""nofollow noreferrer"">Higher Operads, Higher Categories.) It strikes me that the problem might be simplicial sets themselves; are there some more exotic combinatorial objects that are better suited to capturing unbiased compositions? I'm aware of the existence of things like opetopes, but I have no idea if they're relevant to this particular issue.

http://front.math.ucdavis.edu/0305.5049"">Higher Operads, Higher Categories (which is a good reference for biased and unbiased definitions), seems to imply that the difference between unbiased and biased notions is more technical than foundational. Is this the case, or are some concepts of tensor product or morphism really more suited to a biased or an unbiased interpretation? It seems, for instance, that the theory of Lie algebras of Lie groups is rather firmly planted in a biased definition of group, as it relates to the failure of $2$-fold products to commute. Is there a formulation of Lie algebras that is unbiased? Do biased or unbiased definitions better lend themselves to categorification?

http://front.math.ucdavis.edu/0305.5133"" rel=""nofollow"">this article, which was published in Integers. This gives you quickly a large initial segment of the sequence; you cannot jump directly to $a_{1000000}$.

http://front.math.ucdavis.edu/0306.5124""> http://front.math.ucdavis.edu/0306.5124

http://front.math.ucdavis.edu/0306.5396"" rel=""nofollow"">arXiv:math.CO/0306396 by A Abdesselam and The connection between representation theory and Schubert calculus. Basically, instead of working with representations of $GL(n)$ he works with representations of Vec, which he then applies to the tautological bundle over the Grassmannian. The main result is that this map corresponds (part of) the basis of irreps with the basis of Schubert classes.

http://front.math.ucdavis.edu/0306.5420"" rel=""nofollow""> Kramer, Shelah, Tent and Thomas , they define an algebraic system $A(X)$ as the set $X$ with countably many binary relations $R_\alpha$, for all positive rational $\alpha$: $(x,y)\in R_\alpha$ iff ${\mathrm{dist}}(x,y)<\alpha$. Is this the first paper where this algebraic system was defined?

http://front.math.ucdavis.edu/0307.5082"" rel=""nofollow"">Sherman-Zelevinsky, but I don't see it right now.

http://front.math.ucdavis.edu/0307.5164""> http://front.math.ucdavis.edu/0307.5164, section 6.)

http://front.math.ucdavis.edu/0307.5181"" rel=""nofollow noreferrer"">Frenkel and Szczesny constructed a version of Chiral de Rham on orbifolds, and showed that its cohomology yields the orbifold elliptic genus.

http://front.math.ucdavis.edu/0308.5101"" rel=""nofollow""> http://front.math.ucdavis.edu/0308.5101 , especially the polynomiality you're looking for. Note that that was first proven in [H. Derksen, J. Weyman] ""On the Littlewood-Richardson polynomials,"" http://front.math.ucdavis.edu/0308.5281"">Quantum Groups at Roots of Unity and Modularity. In particular the lesson to learn is that if it takes you a while to sort through which papers use which conventions or to find all the relevant constants attached to Lie algebras, then you really owe it to your readers to put that information in your paper where it's easy to find (preferably in a table).

http://front.math.ucdavis.edu/0309.3208"" rel=""nofollow"">McMahon's enumeration of plane partitions. These deal with infinite products or series. I'd like to know if physical or geometric methods have been used to prove congruences

http://front.math.ucdavis.edu/0309.5137"" rel=""nofollow"">Kallel and Salvatore use the string product to help compute the homology of a mapping space in this paper.

http://front.math.ucdavis.edu/0309.5168"" rel=""nofollow"">review article.

http://front.math.ucdavis.edu/0309.5214"" rel=""nofollow"">The colored Jones function is q-holonomic"", they prove that the colored Jones function is $q$-holonomic. Using techniques of Zeilberger, one can then verify such identities algorithmically. So you need only check the first few terms are equal, and check that both sides of the equation satisfy the same recursion relation, which is given by the non-commutative $A$-polynomial which is Bezrukavnikov and Kaledin? They say specifically that they couldn't find any good references and thus had to write up several things themselves.

http://front.math.ucdavis.edu/0309.5427"">""little cubes and long knots"" paper. So this monoid operation is just the connect-sum operation, suitably jazzed-up to be strictly associative.

http://front.math.ucdavis.edu/0309.5427"">""little cubes and long knots"". In particular, you can think of the Vassiliev spectral sequence as being an invariant of $\Omega BK$, not $K$. From the point of view of Vassiliev invariants this isn't such a major insight as $\pi_0 \Omega BK$ is the group-completion of the monoid $\pi_0 K$, so it's just a free abelian group on countably-many generators.

http://front.math.ucdavis.edu/0309.5433"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/0309.5433.

http://front.math.ucdavis.edu/0310.5056"">""Complexes of Graph Homomorphisms.""

http://front.math.ucdavis.edu/0310.5237""> http://front.math.ucdavis.edu/0310.5237, by Costenoble and Waner. http://front.math.ucdavis.edu/0310.5297"" rel=""nofollow"">arXiv:0310.5297, Yuval Peres and Balin Virag study the roots of random power series, $f(z) = \sum a_n z^n$ (where the $a_n$ are Gaussian with mean 0 and variance 1) and show that correlations of the roots are determined by the Bergman kernel http://front.math.ucdavis.edu/0310.5381"" rel=""nofollow"">paper of Ng is false. However, http://front.math.ucdavis.edu/0310.5414"" rel=""noreferrer"">quartic surface, we know one side of mirror symmetry holds when $k$ is the rational Novikov field over $\mathbf{C}$, $\Lambda_{\mathbf{Q}}$. Precisely, we have an equivalence between the idempotent-completed derived Fukaya category of a smooth quartic surface over $\mathbf{C}$, with coefficients in $\Lambda_{\mathbf{Q}}$, and the bounded derived category of the mirror of a smooth quartic surface over $\Lambda_{\mathbf{Q}}$. Here it seems perfectly plausible to replace $\mathbf{C}$ by $k$ again. However, there is a significant difference with the previous example. For $\mathbf{P}^2$, we never had to worry about convergence of the power series defining the products in the Fukaya category thanks to the exactness of everything in sight. But, here a lot of important questions are over $\mathbf{C}$ and depend on convergence. So it would make the most sense to take something like a $p$-adic field for $k$.

http://front.math.ucdavis.edu/0311.4705"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/0311.4705) substantially generalized this framework, and Kenyon and Okounkov (variety proved that KTG is finitely generated by two elements- the tetrahedron with its two possible vertex-orientations.
http://front.math.ucdavis.edu/0312.4730"" rel=""nofollow"">here. They classify case-by-case the possible good gradings for $e$. One of these is the Dynkin grading, which is even iff the labels on the Dynkin diagram of $e$ (or its orbit) are all even. In some cases but not others there are other good gradings.

http://front.math.ucdavis.edu/0312.5007"" rel=""nofollow""> http://front.math.ucdavis.edu/0312.5007

http://front.math.ucdavis.edu/0401.5108"" rel=""nofollow"">this paper of Backelin and Kremnitzer.

http://front.math.ucdavis.edu/0401.5317"" rel=""nofollow"">Orellana-Ram. Actually, they consider the action of the affine braid group on $M\otimes V^{\otimes n}$, but you can recover your case by taking $M$ to be the trivial module. I believe that this is is a semisimple representation (assuming you mean $V$ to be finite dimensional), but in any case it is all spelled out in the paper above.

http://front.math.ucdavis.edu/0401.5401""> http://front.math.ucdavis.edu/0401.5401 by Wlodarczyk. This article has the advantage that it is self-contained and complete and relatively short. It lacks discussion of examples in higher dimensions and motivation that other papers have, as it is quite to the point.

http://front.math.ucdavis.edu/0403.5212"" rel=""nofollow"">Universal Characteristic Factors and Furstenberg Averages, Tamar Ziegler talks about ""unconventional ergodic averges"" which were used in Furstenberg's proof of Szemeredi's theorem. I had trouble understanding the notion of ""characteristic factor"" in dynamical system, so I focused on some of the earlier examples in her paper.

http://front.math.ucdavis.edu/0403.5263"">proof of Cohn and Kumar for the densest lattice in 24 dimensions, checking an automated proof can be carried out (again usually using computers) with less effort compared to the effort in finding the proof.

http://front.math.ucdavis.edu/0403.5496"" rel=""nofollow noreferrer"">here. Now that his program seems to have been completed, it is natural to renew the question in the header:

http://front.math.ucdavis.edu/0405.5030"">asymptotic cones or boundaries of metric spaces). I wonder if similar objects can be obtained as shapes minimizing some kind of energy functional. This may lead to new constructions in geometric group theory.

http://front.math.ucdavis.edu/0405.5233"" rel=""noreferrer"">Nick Proudfoot's thesis). These are very nice symplectic manifolds (hyperkahler and exact, in particular), so I feel like their Fukaya categories should themselves be nice, but I've never found a good reference on them.

http://front.math.ucdavis.edu/0405.5285"" rel=""nofollow noreferrer"">BDPP.

http://front.math.ucdavis.edu/0405.5568"" rel=""nofollow"">myself and Calegari-Gabai, thus defining the ending lamination for general Kleinian groups. In the compressible case, the ending lamination must lie in the Masur domain.

http://front.math.ucdavis.edu/0406.5242"" rel=""nofollow"">Proposition 2.1 of this paper.

http://front.math.ucdavis.edu/0406.5269"" rel=""nofollow"">Cimasoni and Turaev have a very natural generalization of the Alexander module that's hovering around your concerns.

http://front.math.ucdavis.edu/0406.5384"" rel=""nofollow"">Roth and Vakil.

http://front.math.ucdavis.edu/0406.5407"">I made a stab at trying to prove this, but I never published it since Walter Neumann pointed out to me that a generic degenerate group is transcendental, since there are uncountably many ending laminations, but countably many algebraic groups). Then either the group is geometrically finite, and one should be able to search for a finite-sided fundamental domain, or else it is the fiber of a fibration, and one should be able to compute a finite-volume hyperbolic 3-orbifold fibering over the circle, such that the fiber group is generated by the matrices.

http://front.math.ucdavis.edu/0407.5306"">my paper with Ron Graham) but it isn't known if this is all instances of cosecant sums being zero.

http://front.math.ucdavis.edu/0408.5141"">Helfgott's paper how to do this in general.

http://front.math.ucdavis.edu/0408.5337"" rel=""noreferrer""> section 8.3 of Toën's paper which treats DG enhancements but shows that the philosophy of integral transforms and ""bimodules"" is a very general one.

http://front.math.ucdavis.edu/0410.5043"">this survey of Wall, and this list of questions by Hillmann.

http://front.math.ucdavis.edu/0410.5215"">Kotschick proved http://front.math.ucdavis.edu/0411.5016"" rel=""nofollow""> http://front.math.ucdavis.edu/0411.5016

http://front.math.ucdavis.edu/0411.5039"" rel=""nofollow"">constructed such a group with two conjugacy classes.

http://front.math.ucdavis.edu/0411.5039"" rel=""nofollow"">Osin's infinite group with 2 conjugacy classes every proper subgroup is big. Of course if you do not care about the number of generators, you can consider the (much easier) infinitely generated group constructed by Higman-Neumann-Neumann where all non-identity elements are conjugate. There also every proper subgroup is big.

http://front.math.ucdavis.edu/0411.5350"" rel=""nofollow"">Proudfoot and myself. You should be warned that all those papers talk about hyperplane arrangments; you should turn a graph into a hyperplane arrangment by taking a variable for each vertex, and a hyperplane for each edge given by equating the variables at opposite ends.

http://front.math.ucdavis.edu/0411.5436"">in this reference. But very few integral homotopy or homology groups have been computed as of yet.

http://front.math.ucdavis.edu/0411.5469"" rel=""nofollow""> http://front.math.ucdavis.edu/0411.5469""> http://front.math.ucdavis.edu/0411.5469 .

http://front.math.ucdavis.edu/0411.5469 for some history, and several good references. Moreover, Ravi describes how to build an explicit cover of P^2 in characteristic p which does not deform to characteristic 0. Basically, the idea is to take a collection of lines in P^2 which doesn't deform to characteristic 0 and take a branched cover over those lines. For example, you could take that p^2+p+1 lines that have coefficients in F_p.

http://front.math.ucdavis.edu/0411.5605"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/0411.5605. Using that approach one would need to construct an embedding of $F$ into a Hilbert space with compression function $\gg \sqrt{n}$. That approach was killed in http://www.numdam.org/item/AIF_2016__66_6_2435_0/ where it was proved that the compression function cannot exceed $\sqrt{n}$. Another approach from https://arxiv.org/abs/1008.3868 uses the so called dimension growth. We hoped that the dimension growth of $F$ is subexponential which would imply $A$ (see of examples this article (last modified December 2004) suggests the Wikipedia article is reasonably up-to-date.

http://front.math.ucdavis.edu/0412.5283"">[arXiv version]

http://front.math.ucdavis.edu/0412.5329"" rel=""noreferrer"">Tevelev describes this as well known.

http://front.math.ucdavis.edu/0501.5094"" rel=""noreferrer"">Derived categories of sheaves: a skimming.

http://front.math.ucdavis.edu/0501.5246"" rel=""nofollow"">Lam and Postnikov.

http://front.math.ucdavis.edu/0501.5247"" rel=""nofollow"">Fedosov quantization in positive characteristic? That has a page or so on formal geometry in characteristic p.

http://front.math.ucdavis.edu/0501.5497"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/0501.5497 .

http://front.math.ucdavis.edu/0502.5100"" rel=""nofollow"">here. It includes a more extensive list of related papers including those already mentioned in the question. (All of this was heavily influenced by conversations I had with Roman Bezrukavnikov, but the program sketched remains speculative.)

http://front.math.ucdavis.edu/0502.5282"">paper for some partial results!

http://front.math.ucdavis.edu/0502.5301"">""Noncommutative geometry and quiver algebras.""

http://front.math.ucdavis.edu/0502.5366"">expository note on the projective case, which you might find helpful as well.

http://front.math.ucdavis.edu/0502.5404"" rel=""nofollow"">A cylindrical reformulation of Heegaard Floer homology"" will let you easily construct examples of high genus surface with index 1, and a little more playing around should let you see that some of these must actually have representatives.

http://front.math.ucdavis.edu/0502.5405"" rel=""nofollow"">Generators of D-modules in positive characteristic

http://front.math.ucdavis.edu/0502.5408"" rel=""nofollow"">interlace (is a real symmetric matrix, or Hermitian). http://front.math.ucdavis.edu/0503.5040"" rel=""nofollow"">characters of the symmetric group $S_n$) form a Hopf algebra. Is there a corresponding topological structure?

http://front.math.ucdavis.edu/0503.5605"" rel=""nofollow""> http://front.math.ucdavis.edu/0503.5605

http://front.math.ucdavis.edu/0503.5609"" rel=""nofollow""> http://front.math.ucdavis.edu/0503.5609 . Let $R(S^1) = Z[t^\pm]$, so the restriction map $K_T(S^2) \to K_T($fixed points$) = Z[t_1^\pm] \oplus Z[t_2^\pm]$ hits those pairs $(p(t_1),q(t_2))$ such that $p(1) = q(1)$.

http://front.math.ucdavis.edu/0503.5739"" rel=""noreferrer"">here, along with papers by his student T. Xue. A serious challenge when $p$ is bad is to find a uniform explanation for the failure of the numbers of unipotent classes and nilpotent orbits to agree in some cases: the details were worked out by Holt-Spaltenstein and others. In spite of this breakdown in $G$-equivariance, a natural question can be raised:

http://front.math.ucdavis.edu/0504.5206"">Here is a mass of torsion computations for the homology of the long knot space.

http://front.math.ucdavis.edu/0505.5244"" rel=""nofollow"">open question, whether there is a convex-cocompact map (in particular injective) $\pi_1(\Sigma_h)\to Mod(g)$. If this exists, the $\pi_1$ of the associated bundle is a word-hyperbolic group. In this case, there is a theorem of Sela which allows one to algorithmically distinguish the fundamental groups, and therefore determine the homotopy type of the associated manifolds. However, this could be a theory of the empty set, since no examples are known!

http://front.math.ucdavis.edu/0505.5354"">here, some slides of Paugam on the functional equation, and also the later chapters of Manin-Panchishkin. Some of the key names if you want to find more references: Deninger, Connes, Consani, Marcolli; most of them have lots of stuff on their webpages and on the arXiv.

http://front.math.ucdavis.edu/0506.5577"" rel=""noreferrer"">proof with Francesco Costantino, also direct and geometric. You take the compact 3-manifold and look at a generic map to $\mathbb{R}^2$. The preimage of a generic point is a disjoint union of circles, which bounds a convenient canonical surface (a union of disks). Take these disks as the start of your 4-manifold. In codimension one singularities, two of these circles can merge, and the preimage of a little transversal is a pair of pants, which can be filled in with a 3-sphere (together with the disks already attached). In codimension 2, there are only two different interesting local models, and both can be filled in canonically with a 4-ball.

http://front.math.ucdavis.edu/0507.4707"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/0507.4707) found a beautiful description of the variational problem for lozenge tilings in terms of the complex Burgers equation. This leads to explicit descriptions of cases like the cardioid in Joseph's answer.

http://front.math.ucdavis.edu/0507.5070"" rel=""nofollow""> http://front.math.ucdavis.edu/0507.5070, Colliot-Th'el`ene http://front.math.ucdavis.edu/0507.5537"" rel=""nofollow""> http://front.math.ucdavis.edu/0507.5537

http://front.math.ucdavis.edu/0507.5573"" rel=""nofollow"">Densities in free groups and $\mathbb {Z}^ k $, Visible Points and Test Elements http://front.math.ucdavis.edu/0508.5003"" rel=""nofollow"">Representations of shifted Yangians and finite W-algebras. This theorem also gives a construction, as does B&K's http://front.math.ucdavis.edu/0508.5272 ) and more should fit the bill.

http://front.math.ucdavis.edu/0508.5332"" rel=""noreferrer"">these notes, but also pretty much everywhere else that proves resolution of singularities.

http://front.math.ucdavis.edu/0508.5397"" rel=""nofollow""> http://front.math.ucdavis.edu/0508.5397.

http://front.math.ucdavis.edu/0509.5681"">This paper by Cohen and Norbury discussed Steenrod operations, including Adem relations and Cartan formulae.

http://front.math.ucdavis.edu/0511.5001"" rel=""nofollow"">Anna Lenzhen showed that there are Teichmuller geodesics which do not limit to $PMF$ (in fact, I think it was known before by Kerckhoff that the visual compactification is not Thurston's compactification).

http://front.math.ucdavis.edu/0511.5248"" rel=""nofollow noreferrer"">Harmonic algebraic curves and noncrossing partitions

http://front.math.ucdavis.edu/0511.5392"" rel=""nofollow""> http://front.math.ucdavis.edu/0511.5392

http://front.math.ucdavis.edu/0511.5714"" rel=""nofollow noreferrer"">here (see 5.10), which is Abels' group over the ring $\mathbf{F}_p[t,1/t]$, and which probably be used to provide a negative answer to the question. Define the group $G$ as the group of matrices

http://front.math.ucdavis.edu/0601.5093"" rel=""nofollow""> http://front.math.ucdavis.edu/0601.5093

http://front.math.ucdavis.edu/0601.5202"">here.

http://front.math.ucdavis.edu/0601.5229"">here for Craig's paper.

http://front.math.ucdavis.edu/0601.5522"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/0601.5522), this is known to imply that $(G,F)$ is a symmetric space and so that the metric $F$ is bi-invariant.

http://front.math.ucdavis.edu/0601.5540"" rel=""nofollow"">paper of T.-J. Li and myself: we observe http://front.math.ucdavis.edu/0602.5215"" rel=""nofollow""> my paper ). These are not quite Turing machines, but can be easily converted into Turing machines. It is defined by a collection of words $r_1,...,r_n$. The commands are $q\to r_i^{\pm 1} q$, $q\to aqa^{-1}$ where $a$ is any letter of the alphabet, $q$ is the (only one!) state letter. Unlike a Turing machine, a Miller machine works with words which may contain inverses of the letters, and reduces a word after every step (this is a particular case of the so-called S-machines). The word $w$ is accepted if the machine takes $wq$ to $q$. Clearly the set of words accepted by the Miller machine is exactly the set of words equal to 1 modulo relations $r_i=1$, $i=1,...,n$.

http://front.math.ucdavis.edu/0602.5394"" rel=""nofollow""> http://front.math.ucdavis.edu/0602.5394.

http://front.math.ucdavis.edu/0602.5626"" rel=""nofollow"">branch varieties is kind of like a higher dimensional version of the moduli space of stable maps. (Although you should be warned that the moduli space of stable maps is not a special case of the moduli space of branch varieties. In the moduli space of branch varieties, there are never any maps with positive dimensional fibers.)

http://front.math.ucdavis.edu/0603.5102"">preprint of Jesse Johnson. He http://front.math.ucdavis.edu/0603.5218"" rel=""nofollow noreferrer"">a work by Jeff Kahn and me about threshold behavior of monotone properties. The problem is related to an appealing conjecture about random graphs.

http://front.math.ucdavis.edu/0603.5218"" rel=""nofollow noreferrer"">Conjecture: Consider a random graph G in G(n,p) and the graph property: G contains a copy of a specific graph H. (Note: H depends on n; a motivating example: H is a Hamiltonian cycle.) Let q be the minimal value for which the expected number of copies of H' in G is at least 1/2 for every subgraph H' of H. Let p be the value for which the probability that G contains a copy of H is 1/2. Conjecture: p/q = O(log n).

http://front.math.ucdavis.edu/0603.5218"" rel=""nofollow noreferrer"">Thresholds and expectation thresholds by Kahn and me and are mentioned in this MO question. If true these conjectures will imply that the threshold for connectivity will be below logn/n (of course, we do not need it for this case...), and the proof will probably will at best be much much more complicated then existing proofs.

http://front.math.ucdavis.edu/0603.5239"" rel=""nofollow"">a paper on near-extremal phenomena in this setting.

http://front.math.ucdavis.edu/0603.5475"" rel=""nofollow"">Mazorchuk, Ovsienko and Stroppel (though I assume some version of it was known earlier). The category of graded representations of $A^!$ is the same as the (abelian!) category of linear projective complexes over $A$, and vice versa. So, in Dag Oskar Madsen's answer, I would write not $\mathbb{C}[n]\langle n\rangle$, but rather its projective resolution $A^![n+1]\langle n+1\rangle\overset{x}\to A^![n]\langle n\rangle$. Similarly, the $A^!$ modules $\mathbb{C}[x]/(x^{n+1})$ are sent by Koszul duality to the complexes

http://front.math.ucdavis.edu/0604.5054"" rel=""nofollow"">Caldero-Zelevinsky, up to a monomial change of variables. (I won't try to get the monomial change of variables right.) It is http://front.math.ucdavis.edu/0604.5379"" rel=""noreferrer"">Nadler-Zaslow

http://front.math.ucdavis.edu/0604.5400"" rel=""noreferrer"">proved that finite-index subgroups of finitely generated profinite groups are open. This implies that http://front.math.ucdavis.edu/0604.5405"" rel=""nofollow noreferrer"">0604.5405.

http://front.math.ucdavis.edu/0605.5069"" rel=""nofollow"">A family of embedding spaces. The result is that the space of embeddings of $S^j$ in $\mathbb R^n$ has the homotopy-type of a bundle:

http://front.math.ucdavis.edu/0605.5069"">A Family of Embedding Spaces. The primary tool used to prove it is what's called the embedding calculus due to Goodwillie, Klein and Weiss.

http://front.math.ucdavis.edu/0605.5217"" rel=""nofollow"">""Schur-Weyl duality for higher levels"".

http://front.math.ucdavis.edu/0605.5431"" rel=""nofollow noreferrer"">here.)

http://front.math.ucdavis.edu/0606.5013""> http://front.math.ucdavis.edu/0606.5013""> http://front.math.ucdavis.edu/0606.5013)

http://front.math.ucdavis.edu/0606.5013. But in general t-structures on $D_{qc}(X)$ do not descend, and even if they do, it might be hard to prove.

http://front.math.ucdavis.edu/0606.5169"" rel=""nofollow noreferrer"">Polynomials, meanders, and paths in the lattice of noncrossing partitions

http://front.math.ucdavis.edu/0606.5169"" rel=""nofollow"">Polynomials, meanders, and paths in the lattice of noncrossing partitions, they talk about sequences of non-crossing matchings related by ""flips"".

http://front.math.ucdavis.edu/0607.5446"" rel=""nofollow""> http://front.math.ucdavis.edu/0607.5446 for details and proofs.

http://front.math.ucdavis.edu/0608.5143"" rel=""nofollow"">here's a survey by Kaledin. If you read his papers, you'll see lots of modern algebraic geometry; theorems like the local existence of tilting generators depend on reduction to characteristic $p$.

http://front.math.ucdavis.edu/0608.5276"">Thomas and Yong for details.

http://front.math.ucdavis.edu/0608.5356"" rel=""nofollow"">this paper of Albers and Frauenfelder. If you carefully choose the size of the blowup (so that the proportionality constant on the exceptional sphere is the same as the monotonicity constant for $L$), then it should be possible to arrange for $L$ to lift to a monotone Lagrangian torus in the blowup. (However for a generic size blowup this probably won't work.)

http://front.math.ucdavis.edu/0608.5635"" rel=""nofollow"">Joe Masters' paper. Given a 1-relator group presentation, realize the free group as the fundamental group of a compact surface (with boundary), and the relator as an immersed loop in this surface. Choose such a surface so that the self-intersection number of the loop representing the relator is minimal. Then Masters' proof shows that this self-intersection number decreases after each (non-trivial) HNN extension in the Magnus-Moldavansky hierarchy (for the base case of an embedded loop on a surface, notice that the 1-relator group is either free or a surface group if the loop is parallel to the only boundary component). I think one can at least bound this self-intersection number from above quadratically in the length of the relator, so this gives a crude estimate.

http://front.math.ucdavis.edu/0609.5388""> http://front.math.ucdavis.edu/0609.5388).

http://front.math.ucdavis.edu/0609.5392"" rel=""nofollow noreferrer"">translation surface.

http://front.math.ucdavis.edu/0609.5764"" rel=""noreferrer""> http://front.math.ucdavis.edu/0609.5764 (the original reference for Postnikov's work) as well as this paper for an introduction (as well as subsequent papers by Boyarchenko and Boyarchenko-Drinfeld).

http://front.math.ucdavis.edu/0609.5846"" rel=""nofollow"">a paper about this question a few years ago.

http://front.math.ucdavis.edu/0610.5203"" rel=""nofollow"">BCHM, Corollary 1.4.3 and also KK, Theorem 3.1. (I've been told more general statements exist also, but I don't know a reference).

http://front.math.ucdavis.edu/0610.5205"" rel=""nofollow"">a paper about this a few years back, which I think is a reasonable starting place for the subject, which actually has quite a long history, and a reasonably extensive literature.

http://front.math.ucdavis.edu/0610.5408"" rel=""nofollow noreferrer"">1] The Fourier transform takes dirac combs supported on a lattices $\Gamma$ to a dirac comb supported on the dual lattices: http://front.math.ucdavis.edu/0610.5437"" rel=""noreferrer"">this paper. We do not discuss the application to $\infty$-algebras as Bruno does in much greater generality. (We were interested in using explicit models to be able to compute, in particular in the long exact sequence of a fibration as we do in a sequel to this paper on Hopf invariants.)

http://front.math.ucdavis.edu/0610.5570"" rel=""noreferrer"">of Lee and Parker.

http://front.math.ucdavis.edu/0610.5591"" rel=""nofollow""> http://front.math.ucdavis.edu/0610.5591, as well as many others by Steve and/or his collaborators. Most of the arXiv papers have subject listing RT (some also consider quantum analogues under QA). But some predate arXiv; there has been a lot of study of decomposition numbers of symmetric groups in prime characteristic, for example, using what little is known about modular representations of GL$_n$. Not having gone far with this literature myself, I'd suggest that you start the inquiry with available papers and then maybe raise narrower questions here.

http://front.math.ucdavis.edu/0610.5839"" rel=""nofollow"">goertz.

http://front.math.ucdavis.edu/0611.5205"" rel=""nofollow"">this preprint.

http://front.math.ucdavis.edu/0611.5451"" rel=""nofollow""> http://front.math.ucdavis.edu/0611.5451 for some large-scale numerical experiments, as well as references to many other papers in the literature.

http://front.math.ucdavis.edu/0611.5771"" rel=""nofollow"">article and go over the references therein. It is written with exactly similar intentions you have asked for.

http://front.math.ucdavis.edu/0612.5032"" rel=""nofollow noreferrer"">proved that, in characteristic $0$, if $A$ is a non-commutative crepant resolution, then $R$ has rational singularity. The definition of NCCR is stronger, but if, for example, $R$ is Gorenstein of dimension $2$, it coincides with my version. So a counterexample is something like $R=k[x,y,z]/(x^3+y^3+z^3)$, which is a non-rational hypersurface.

http://front.math.ucdavis.edu/0612.5082"">here.

http://front.math.ucdavis.edu/0612.5085"" rel=""noreferrer"">in this paper (based again on approximation by polyhedra). http://front.math.ucdavis.edu/0612.5399"" rel=""noreferrer"">Nadler and $\zeta(2)$ using the amoeba of $1 + z + w = 0$. Has this ever been generalized to higher zeta-values? How might one compute $\zeta(2n)$ this way?

http://front.math.ucdavis.edu/0701.5277"">Cheptea-Habiro-Massuyeau consider a category whose morphisms are cobordisms $M$ between closed oriented surfaces $F_+$ and $F_-$, where we choose Lagrangian subgroups $A_{\pm}$ of $H_1(F_\pm)$ correspondingly, and where we require that $H_1(M)=m_-(A_-)+m_+H_1(F_+)$ and that $m_+(A_+)\subseteq m_-(A_-)$ in $H_1(M)$ (the $m_\pm$ are inclusion maps). Similar conditions are imposed in many other papers.
http://front.math.ucdavis.edu/0701.5365"" rel=""nofollow noreferrer""> lacunary hyperbolic but not hyperbolic groups given by presentations satisfying small cancelation conditions or their generalizations are infinitely presented since every finite subpresentation of their presentation defines a hyperbolic group.

http://front.math.ucdavis.edu/0701.5365"" rel=""nofollow"">lacunary hyperbolic groups. Additionally, have a look at Olshanskii's book Geometry of defining relations in groups. In this book many such examples are generated that solve various problems.

http://front.math.ucdavis.edu/0701.5365""> http://front.math.ucdavis.edu/0701.5365). Let $r_1,r_2,...$ be the presentation of $G$. Then $G$ is commutative transitive (it is easily deduced from the fact that $G$ is an inductive limit of hyperbolic groups and surjective homomorphisms). Now the group $G'$ given by the same presentation but without $r_1$ is again lacunary hyperbolic, $G$ is a factor-group of $G'$ over the normal subgroup $N$ generated by $r_1$. It is possible to prove that $N$ is free. Indeed, if some product of conjugates of $r_1$ is equal to 1 in $G$, consider the corresponding van Kampen diagram. The boundary of that diagram has parts labeled by $r_1$ and parts labeled by the conjugators. By Greendlinger lemma, if the diagram has cells, it must have a cell with more than, say, $90\%$ of its boundary common with the boundary of the diagram (take the small cancelation condition $C'(1/300)$). Then more than a half of that part of the boundary must be inside a conjugator, the conjugator can be shortened, and a shorter product of conjugates of $r_1$ is equal to 1 in $G'$. Since $G'$ is lacunary hyperbolic again and satisfies the same small cancelation condition as $G$, we can repeat the construction. Since the presentation is infinite, the process will continue indefinitely.

http://front.math.ucdavis.edu/0701.5462"">here. Obviously it's difficult to sort out the history and motivation to everyone's satisfaction, but Kleiman got enough feedback along the way to be reliable in his version.

http://front.math.ucdavis.edu/0701.5664"" rel=""noreferrer"">of surfaces. Then if $a\in H^2(M)\cong H^2(N)$ is Poincare dual to the pullback of the hyperplane class in $\mathbb{C}P^2$, $a$ will have minimal genus zero in $M$ but positive minimal genus in $N$.

http://front.math.ucdavis.edu/0702.5211"" rel=""noreferrer"">exotic rational symplectic Misère canonical forms of partizan games. A misere game is where the last person to move loses rather than wins.

http://front.math.ucdavis.edu/0704.0091"">this paper. Ashot is sometimes on MO, perhaps he can give more details. If not, you can ask him directly.

http://front.math.ucdavis.edu/0704.0649"">Derksen-Weyman-Zelevinsky for the precise definitions.) [DWZ] show that the space of deformations of (Q,S) is k[[Q]]/(J(S) + [,]) where [,] is the vector space (NOT usually an ideal) spanned by commutators. They define (Q,S) to be rigid if this vector space is spanned by the empty cycle.

http://front.math.ucdavis.edu/0704.1378"" rel=""noreferrer"">arXiv) for some nice discussion.

http://front.math.ucdavis.edu/0704.1378""> http://front.math.ucdavis.edu/0704.1378 exhibits a triangulated category $\mathcal{C}$ such there are no nontrivial exact functors from $\mathcal{C}$ to any of the standard examples of triangulated categories, or in the opposite direction. This means in particular that there is no way to define a 'representable' functor $F_{\mathcal{C}}(x,-)$.

http://front.math.ucdavis.edu/0704.2055"" rel=""nofollow"">Biased View of Symplectic Cohomology,"" see also Remark 5.7 of Bourgeois and Oancea's $1/4$ pinching theorem of Brendle-Schoen.

http://front.math.ucdavis.edu/0705.0998"">this paper by Jessica Striker regarding the alternating-sign-matrix polytope.

http://front.math.ucdavis.edu/0705.4571"">Twisted Whittaker model and factorizable sheaves, Selecta Math. (N.S.) 13 (2008), no. 4, 617--659.

http://front.math.ucdavis.edu/0706.2501"" rel=""noreferrer""> http://front.math.ucdavis.edu/0706.2501 (an article by Postnikov, Speyer, and Williams with more of an emphasis on matchings and flows). In this setting one has Plucker relations that are essentially the same thing as Kuo's graphical condensation.

http://front.math.ucdavis.edu/0706.3937"" rel=""nofollow""> http://front.math.ucdavis.edu/0706.3937 and the last section in maximum overhang" by Mike Paterson, Yuval Peres, Mikkel Thorup, Peter Winkler and Uri Zwick:

http://front.math.ucdavis.edu/0707.1014"" rel=""nofollow"">this paper, Ebert proves that in a stable range we have H_3 of the mapping class group equal to Z/12Z and H_4 equal to Z^2. He does this by using the fact that Madsen and Weiss's work identifies the infinite loop space (Mod_{\infty})^+ with a space whose first few homotopy groups are known. Ebert then builds with his bare hands the first few stages of the Postnikov tower for this space.

http://front.math.ucdavis.edu/0707.2003"" rel=""nofollow"">the paper Geordie Williamson and I wrote on the subject, you'll see that our theorems identify the Hochschild homology of k[t] with the equivariant cohomology of the circle with a trivial circle action. Thus, the bits in degree 0 and 1 correspond to the cohomology of the circle, and the fact that you get k[t] in each corresponds to the fact that k[t] is the cohomology of the classifying space of the circle as a topological group.

http://front.math.ucdavis.edu/0707.2085"" rel=""nofollow""> http://front.math.ucdavis.edu/0707.2085

http://front.math.ucdavis.edu/0707.4522"" rel=""nofollow"">theorem of mine. Thus, for any element in the group, there is a finite-index subgroup for which it is homologically non-trivial. This property passes to subgroups, in which case the fundamental group of the complement of Fox's stitch has the property that there is a finite-index subgroup with infinite abelianization (in fact, a non-trivial homomorphism to $\mathbb{Z}$).

http://front.math.ucdavis.edu/0708.2757"" rel=""nofollow"">Twisted automorphisms of Hopf algebras. In Davydov's other paper, Twisted automorphisms of group algebras, he describes this group in the case that $\lvert G \rvert$ is relatively prime to 6. (The proposed description I gave in the earlier version of this answer fails in general because $\operatorname{Out}(G)$ is not in general a normal subgroup of $\operatorname{Aut}_{\textbf{Tw}}(k[G])$.)

http://front.math.ucdavis.edu/0708.2851"">functoriality for Lagrangian correspondences in Floer homology

http://front.math.ucdavis.edu/0709.1286"" rel=""nofollow"">here.

http://front.math.ucdavis.edu/0709.3202"" rel=""nofollow noreferrer"">produced recently proof, but a flaw emerged.

http://front.math.ucdavis.edu/0709.3534""> http://front.math.ucdavis.edu/0709.3534 (Meridional Almost Normal Surfaces in Knot Complements by Robin Wilson)

http://front.math.ucdavis.edu/0710.0032"" rel=""nofollow"">Extended TQFT's and Quantum Gravity, Ph.D Thesis (University of California, Riverside). http://front.math.ucdavis.edu/0710.0926"" rel=""nofollow"">paper with Healy and Gortler we go through the analysis and get specific bounds (in Section 5). We also go through some analysis for global rigidity, but it's for whether the check for generic global rigidity works, not whether the particular framework is actually globally rigid. For concrete bounds there, you'd have to do a little more work.

http://front.math.ucdavis.edu/0710.1262""> http://front.math.ucdavis.edu/0710.1262 (Algorithmically Detecting the bridge number for hyperbolic knots by Alex Coward)

http://front.math.ucdavis.edu/0710.4978"" rel=""noreferrer"">proved via non-standard methods:

http://front.math.ucdavis.edu/0711.0191"">Breslin), then gluing tetrahedra together in all possible ways, and computing whether they are arithmetic e.g. via Snap.

http://front.math.ucdavis.edu/0711.4079""> Schubert calculus and representations of general linear group Mukhin-Tarasov-Varchenko give another answer. They construct any algebra $ \mathcal{B} $ called the Bethe algebra, which acts on a tensor product multiplicity space $ Hom(V_\lambda, V_{\lambda_1} \otimes \cdots \otimes V_{\lambda_m}) $, depending on parameters $ b_1, \dots, b_n$. They prove that the image $ A $ of the Bethe algebra acting on this vector space has the same dimension of this vector space (for generic $ b_i $ you get all diagonal matrices with respect to some basis). Then they prove this algebra $ A $ is isomorphic to the functions on an scheme-theorectic intersection of $n+1 $ Schubert varieties corresponding to the $ \lambda_i$, with respect to flags given by the $ b_1, \dots, b_n $.

http://front.math.ucdavis.edu/0712.1709"">papers here by Bryant, Dunajski, and Eastwood.

http://front.math.ucdavis.edu/0801.0803"">Dinkelbach-Leeb.

http://front.math.ucdavis.edu/0801.0803%20"" rel=""noreferrer"">Dinkelbach and Leeb for spherical, hyperbolic, and $S^2\times R$ metrics. http://front.math.ucdavis.edu/0801.0873""> http://front.math.ucdavis.edu/0801.0873).

http://front.math.ucdavis.edu/0801.3025"" rel=""nofollow""> http://front.math.ucdavis.edu/0801.3025

http://front.math.ucdavis.edu/0801.3306"" rel=""nofollow noreferrer"">Abelian Sandpile Model and noticed the identity element of the sandpile group on the square has self-similar components.

http://front.math.ucdavis.edu/0802.2225"">Comparative smootheology give a nice overview of cartesian closed settings of smooth spaces.

http://front.math.ucdavis.edu/0802.4074"" rel=""nofollow"">computed for twist knots.

http://front.math.ucdavis.edu/0802.4302"" rel=""noreferrer"">Sam Payne's article, which discusses the toric case. The first shows that it's true for flag manifolds, and the second that it's not true for all Schubert varieties.

http://front.math.ucdavis.edu/0803.0341"">Hilbert schemes of 8 points

http://front.math.ucdavis.edu/0803.0720"" rel=""nofollow"">this paper by Keller-Murfet-Van den Bergh.

http://front.math.ucdavis.edu/0803.2616"" rel=""nofollow"">arXiv: 0803.2616.

http://front.math.ucdavis.edu/0804.0579"" rel=""noreferrer"">Tropical Hurwitz Numbers and http://front.math.ucdavis.edu/0804.1396 http://front.math.ucdavis.edu/0805.0563"" rel=""nofollow""> http://front.math.ucdavis.edu/0805.0563

http://front.math.ucdavis.edu/0805.0756"" rel=""noreferrer"">Kollar08 (making this a non-example in some people's mind).

http://front.math.ucdavis.edu/0805.4354"" rel=""nofollow"">""unlinks"" would be one of the most direct generalizations. Beyond the geometric aspect, there's a similar and somewhat more substantial connection to the automorphism group of a free group in this setting.

http://front.math.ucdavis.edu/0805.4354"" rel=""nofollow"">Configuration spaces of rings and wickets"" and Brownstein-Lee ""Cohomology of the group of motions of n strings in 3-space"".

http://front.math.ucdavis.edu/0805.4578"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/0805.4578"">here. Briefly, the Brown-Gersten approach does not work for arbitrary sites, but it works for a class of sites defined in Voevodsky's paper - this class includes Noetherian finite-dimensional spaces. When the B-G approach works, the resulting model structure has better finiteness properties than the Joyal-Jardine model structure, which on the other hand can be defined for simplicial (pre)sheaves on any site.

http://front.math.ucdavis.edu/0805.4578 , where I discovered lemma 4.1 , which I think aswers your question.

http://front.math.ucdavis.edu/0806.3256"">found some cool examples http://front.math.ucdavis.edu/0806.3580"">on the Finding the sum of any series from a given general term on the arXiv. In recent years, this idea has been extended to sums over lattice approximations of convex polytopes $\Delta \cap \mathbb{Z}^n$ as shown in the other responses.

http://front.math.ucdavis.edu/0806.4404"" rel=""noreferrer"">longer arXiv version.

http://front.math.ucdavis.edu/0807.1023"" rel=""nofollow"">here.

http://front.math.ucdavis.edu/0807.3602"" rel=""nofollow"">Parkinson-Ram

http://front.math.ucdavis.edu/0807.4146"" rel=""nofollow""> http://front.math.ucdavis.edu/0807.4146"" rel=""nofollow"">, though that paper does not use 2-categorical language.

http://front.math.ucdavis.edu/0807.5121"">Greg Martin's paper, with some coauthor or other, isn't the state of the art, but it's the source that sticks in my mind.

http://front.math.ucdavis.edu/0808.0739"" rel=""nofollow noreferrer"">Boolean formulae, hypergraphs and combinatorial topology

http://front.math.ucdavis.edu/0808.1176"">Lackenby-Meyerhoff, but I've also shown that there is an algorithm which will determine the finitely many manifolds with $>8$ exceptional Dehn fillings.

http://front.math.ucdavis.edu/0808.1442"" rel=""nofollow"">mock theta functions. Here's another one involving http://front.math.ucdavis.edu/0808.2990

http://front.math.ucdavis.edu/0809.1203"" rel=""nofollow noreferrer"">frequently you can prove SnapPea to be correct. Although I occasionally still try to break SnapPea. There is an algorithm to find the hyperbolic structure on the various hyperbolic bits, I'm not sure what name people will settle on but I like to call it the cusped Manning algorithm (should appear in the JacoFest proceedings, author is Tillman).

http://front.math.ucdavis.edu/0809.1203"" rel=""nofollow noreferrer"">Harriet Moser to prove that SnapPea does give approximations to actual solutions to the hyperbolic gluing equations. The applications of course are pretty broad, this is one on the fairly pure end of the spectrum. Kantorovich was an economist although I do not understand the economics problems he was interested in.

http://front.math.ucdavis.edu/0809.2579"" rel=""nofollow""> http://front.math.ucdavis.edu/0809.2579"">Exercises in the Birational Geometry of Algebraic Varieties http://front.math.ucdavis.edu/0809.2579 and do exercise 66 on DuVal singularities of surfaces. It's good to do by hand if you need practice with blowups, otherwise, just looking at the fact that you get ADE out of canonical surface singularities should motivate the need for Dynkin diagrams, which describe the root systems.

http://front.math.ucdavis.edu/0809.3469"" rel=""nofollow"">arXiv:0809.3469).

http://front.math.ucdavis.edu/0809.4040"" rel=""nofollow"">Morgan-Tian talk about this.

http://front.math.ucdavis.edu/0809.4040"">paper I realized that they prove the geometrization for every compact 3-manifold $M$ with no embedded two-sided projective planes, which was news to me. There is a lot of notation in their paper so I ask

http://front.math.ucdavis.edu/0809.4881""> http://front.math.ucdavis.edu/0809.4881

http://front.math.ucdavis.edu/0810.0066""> http://front.math.ucdavis.edu/0810.0066. I don't know anything about the algebraic category, but I believe that there's interesting stuff there too (as far as I can tell, algebraic stacks are more complicated than smooth ones).

http://front.math.ucdavis.edu/0810.0390"">This paper shows that the answer to 2) is false in the category of finitely presented residually finite groups. As Greg points out, this is different from the category of finitely presented linear groups though.

http://front.math.ucdavis.edu/0810.2346"" rel=""nofollow"">arXiv paper. You'll also find some references to several Jonathan Hillman papers that explore such obstructions.

http://front.math.ucdavis.edu/0810.2346""> http://front.math.ucdavis.edu/0810.2346 Some are geometric, some have incompressible tori.

http://front.math.ucdavis.edu/0810.3146"">an arrow-diagram formula for coefficients of the Conway polynomial by Chmutov, Khoury, and Rossi. In it, he described how to obtain formulae for a Conway polynomial of string links, string links in open-closed surfaces etc. These formulae do not give generalizations of the Alexander polynomial. This is funny, because I always thought that the Alexander polynomial and the Conway polynomial were basically the same, but that turns out not to be the case at all, philosophically.
http://front.math.ucdavis.edu/0810.4392""> http://front.math.ucdavis.edu/0810.4392; but there must be lots of earlier papers).

http://front.math.ucdavis.edu/0811.2215"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/0811.2215

http://front.math.ucdavis.edu/0811.2482"">this paper, one can bound from above the degree of the invariant trace field of an arithmetic hyperbolic 3-manifold with volume $\leq V$. This in turn leads to a lower bound on the injectivity radius $\epsilon(V)$ ( it is conjectured that there is a universal lower bound to the injectivity radius of closed arithmetic 3-manifolds; this is true if one restricts to arithmetic manifolds defined over a number field of bounded degree by Lemma 4.9 and the fact that the Mahler measure of an integral polynomial of bounded degree is bounded). Now construct all manifolds of volume $ \leq V$ with injectivity radius $\geq \epsilon(V)$. All arithmetic manifolds of volume $\leq V$ will appear among this list. One may perform this construction by bounding the number of tetrahedra in a triangulation (see e.g. some reason to be optimistic that Vassiliev invariants can distinguish knots from their inverses. If I recall correctly, he creates a splitting of the homology of various embedding spaces. This does not work for knots in $\mathbb R^3$, but there is an analogy to the 3-dimensional case. Moreover he computes some classes which, if analogous classes existed in the 3-dimensional case they would be orientation-sensitive. He goes so far as to suggest a certain class of Vassiliev invariant would be a productive place to look for inversion-sensitive invariants (see page 35, just before section 17).

http://front.math.ucdavis.edu/0812.0221"" rel=""nofollow""> http://front.math.ucdavis.edu/0812.0221

http://front.math.ucdavis.edu/0812.1407"" rel=""nofollow noreferrer"">""Steenrod homotopy"". The topological homomorphism between $\pi_1(X)$ (with topology as in my comment) and the topological Cech fundamental pro-group is discussed in theorem 6.1, section 5 and elsewhere in ""Steenrod homotopy"".

http://front.math.ucdavis.edu/0812.1407"" rel=""nofollow noreferrer"">"Steenrod homotopy", Lemma 7.3 or Mardesic-Matijevic) definition of an overlay is that it is

http://front.math.ucdavis.edu/0812.1407"" rel=""nofollow""> http://front.math.ucdavis.edu/0812.1407"" rel=""nofollow"">here. Still I doubt that they have been studied per se.

http://front.math.ucdavis.edu/0812.1407 (which includes a simplified proof of the Krasinkiewicz-Minc result).

http://front.math.ucdavis.edu/0812.4161""> here.

http://front.math.ucdavis.edu/0901.0442"" rel=""nofollow"">this paper by Bartels-Lueck.

http://front.math.ucdavis.edu/0901.0665"" rel=""nofollow"">here.

http://front.math.ucdavis.edu/0901.1612"" rel=""noreferrer"">Melvin et al. proved it does. http://front.math.ucdavis.edu/0901.1830"">There is an algorithm to solve equations in such groups, and parameterize the solutions. Since your equation is degree zero in $a,b,x$, if the lift of the solution in $PSL_2\mathbb{Z}$ to $B_3$ solves the equation for one lift, it should work for any other lift. I'm not quite sure though how to determine this uniformly over all lifts of the solution. The solutions are given by Makanin-Razborov diagrams, and they are parameterized by various automorphisms. So I think you just need to check one solution in each equivalence class coming from each orbit.

http://front.math.ucdavis.edu/0901.3992"" rel=""nofollow noreferrer"">Varagnolo-Vasserot the question 1 has an affirmative answer (in equivariant homology). (the maps are not small though, but they resemble the map $\mathfrak{g}'\to\mathfrak{g}$).

http://front.math.ucdavis.edu/0902.0436"">this paper of Benedetti and Ziegler. It is not known if this result extends to graphs of general d-polytopes, or to all subgraphs of graphs of simple d-polytopes, or to dual graphs of all triangulations of (d-1)-spheres. The later question is discussed by Gromov in the paper spaces and questions (p. 33).

http://front.math.ucdavis.edu/0902.0648"" rel=""nofollow""> http://front.math.ucdavis.edu/0902.0648"" rel=""nofollow"">HERE

http://front.math.ucdavis.edu/0902.0648

http://front.math.ucdavis.edu/0902.1294"" rel=""nofollow"">Haagerup subfactor, with principal graph the $3$-long $3$-star in your terminology. Emily Peters has written a bit about this, and it has an this paper. Although it's formulated differently (in terms of random circulant matrices), my result estimates the fraction of $\pm 1$ polynomials of degree $d$ which are divisible by some cyclotomic polynomial of order dividing $d+1$. If $d$ is odd, this fraction is of the order $d^{-1/2}$. If $d$ is even, I derived two different upper bounds which imply that the fraction is smaller than in the even case; in particular, if $d+1$ is prime then $\pm \sum_{k=0}^d x^k$ are (pretty obviously) the only such polynomials.

http://front.math.ucdavis.edu/0902.2480"" rel=""nofollow"">this survey by Lueck, http://front.math.ucdavis.edu/0902.3294"" rel=""nofollow"">paper of Wirth.

http://front.math.ucdavis.edu/0902.3464"" rel=""nofollow""> http://front.math.ucdavis.edu/0902.3464 , meaning that etale locally it is just a disjoint unions of (d many) pancakes. Can we do this generally? Is there some ""connectivity"" conditions on Y for this to work? Is there a different valid definition for degree of an etale cover of stacks?

http://front.math.ucdavis.edu/0903.2281"" rel=""nofollow""> http://front.math.ucdavis.edu/0903.2281

http://front.math.ucdavis.edu/0903.3052"">More recently, Bryant http://front.math.ucdavis.edu/0903.4493"">arXiv:0903.4493. For the corresponding result in the graded setting, following Ryom-Hansen, see http://front.math.ucdavis.edu/0903.5060"" rel=""nofollow""> http://front.math.ucdavis.edu/0903.5060 -- for example one of them is that v is a morphism of $M$-sets).

http://front.math.ucdavis.edu/0903.5060

http://front.math.ucdavis.edu/0904.2797"">Abramovich and Hassett where they call such stacks cyclotomic. If you define ampleness in terms of some other positivity (like Kleiman's criterion, Nakai-Moishezon, etc), then you will have many of the same theorems as in the case of varieties - because more or less this positivity will just be ""pulled back"" from the coarse moduli space. So the answer depends on the situation you are in and the kinds of properties in which you are interested.

http://front.math.ucdavis.edu/0904.3035""> http://front.math.ucdavis.edu/0904.3035 or http://front.math.ucdavis.edu/0904.3153. The answer depends not only on $R$ but also on $n$.

http://front.math.ucdavis.edu/0904.3349"">a paper to the arXiv himself in April of this year. So you could ask him how to pronounce his name, and about his genealogy.

http://front.math.ucdavis.edu/0904.3740"">discrete and continuous determinantal processes. Maybe it's be better to sample a processes directly using Coupling from the Past and other procedures.

http://front.math.ucdavis.edu/0904.4227"" rel=""noreferrer"">this paper might touch on this, though.

http://front.math.ucdavis.edu/0905.0404"">Globally $F$-regular and log Fano varieties due to Karen Smith and myself. Log Fano's are varieties where $-K_X$ is not necessarily ample, but where it is close. Some additional discussion of the lemmas above can also be found here.

http://front.math.ucdavis.edu/0905.0486"" rel=""nofollow"">my paper with Geordie Williamson; it's in Section 4, I think).

http://front.math.ucdavis.edu/0905.0486"" rel=""nofollow"">my second paper with Geordie Williamson.

http://front.math.ucdavis.edu/0905.0837"" rel=""nofollow"">arXiv:0905.0837.

http://front.math.ucdavis.edu/0905.1617"" rel=""nofollow noreferrer"">here, but the published version is somewhat longer. I haven't checked the precise differences, but this is always a hazard when consulting arXiv preprints. The joint work of Melnikov with various people has uncovered many of the known results about singularities of irreducible components of Springer fibers. This builds on work of Francis Fung in type $A$, for example, and mostly deals with aspects that can be formulated combinatorially.

http://front.math.ucdavis.edu/0905.2054"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/0905.2054).

http://front.math.ucdavis.edu/0905.4698"">Riffle shuffles of a deck with repeated cards http://front.math.ucdavis.edu/0906.0290"" rel=""nofollow noreferrer"">my collection of exercises.

http://front.math.ucdavis.edu/0906.0610"">recent preprint, they study infinite reduced words in W, modulo braid and commutation relations. This is a good substitute for a reduced word for the long word in the context of total positivity, as they explain. I think it should also be useful in the context of canonical bases.

http://front.math.ucdavis.edu/0907.4219"" rel=""noreferrer"">preprint giving a model for Floer cohomology of a Lagrangian that has a pairing at the chain level which is cyclically symmetric. There is work underway to extend it to the whole Fukaya category.

http://front.math.ucdavis.edu/0908.0685"">Bridson showed that if a mapping class group of a surface (of genus at least 3) acts on a CAT(0) space, then Dehn twists act as elliptic or parabolic elements. This implies that the mapping class groups of genus $\geq 3$ are not CAT(0) (Edit: as pointed out by Misha in the comments, this was originally proved by Kapovich and Leeb, based on an observation of Mess that there is a non-product surface-by-$\mathbb{Z}$ subgroup of the mapping class group of a genus $\geq 3$ surface). On the other hand, the mapping class group of a genus 2 surface acts properly on a CAT(0) space (this is not surprising, since it is linear). I think it's unresolved whether the mapping class group of genus 2 is CAT(0) though (this is essentially equivalent to the same question for the 5-strand braid group).

http://front.math.ucdavis.edu/0908.1092"" rel=""noreferrer""> http://front.math.ucdavis.edu/0908.1092. For symmetric spectra, the original source is Sagave and Schlichtkrull this.

http://front.math.ucdavis.edu/0908.4187"">results on uniqueness of enhancements give a large class of triangulated categories for which one might lift exact functors to dg-functors and apply Toen's result.

http://front.math.ucdavis.edu/0908.4201"" rel=""nofollow""> http://front.math.ucdavis.edu/0908.4201

http://front.math.ucdavis.edu/0909.1810"" rel=""nofollow"">0909.1810, the cyclotomic KLR algebras, which I strongly believe are symmetric, but after quite a bit of trying, have had no luck with. Anyone else care to try their hand?

http://front.math.ucdavis.edu/0909.1860"" rel=""nofollow"">Singular blocks of parabolic category O and finite W-algebras"", these are called ""S3-varieties."" S3 is for ""Slodowy-Springer-Spaltenstein.""

http://front.math.ucdavis.edu/0909.1984"" rel=""nofollow"">Kleshchev and Ram, and arXiv version). There is a nice reformulation of the conjectures in terms of Arakelov motivic cohomology, by Jakob Scholbach (see articles on his webpage). You might also want to check out some of the articles of Rob de Jeu and his coauthors. In addition, there have been various attempts at new descriptions of the Beilinson regulator, most recently by ""Fusion categories and homotopy theory."" The main results of this paper are proved by formulating their questions in terms of classical obstruction theory on the nerves of certain 3-groupoids. The obstruction theory itself can be justified using elementary fiddling with simplicial sets, as the reference Gregory Arone provided to my earlier question on obstrucion theory reveals. However, I wanted to understand the category theory side of the equation better, which led me to try to formulate things in terms of unbiased monoidal 2-categories.

http://front.math.ucdavis.edu/0909.3140"">Fusion categories and homotopy theory.)

http://front.math.ucdavis.edu/0909.3292"" rel=""noreferrer""> http://front.math.ucdavis.edu/0909.3292, in particular Section 10 for discussion of Stiefel-Whitney classes.

http://front.math.ucdavis.edu/0909.4099"" rel=""nofollow"">even stranger companion where one leg is $7$-long. However, there's actually a subfactor with principal graph a $3$-long $p$-star for every prime $p$!

http://front.math.ucdavis.edu/0909.4526"" rel=""nofollow"">paper on the Gysin sequence

http://front.math.ucdavis.edu/0909.4625""> http://front.math.ucdavis.edu/0909.4625""> http://front.math.ucdavis.edu/0909.4625

http://front.math.ucdavis.edu/0909.4625

http://front.math.ucdavis.edu/0910.0155"" rel=""nofollow"">arXiv:0910.0155

http://front.math.ucdavis.edu/0911.0977"" rel=""nofollow"">Tannaka duality for comonoids in cosmoi. Specializing to your setting, he shows that there is a biadjunction (a weak 2-categorical form of adjunction) between the 2-category of $k$-linear categories equipped with a functor to $\operatorname{FinVect}$, where morphisms are triangles commuting up to specified natural isomorphism, and the usual category of coalgebras (thought of as a 2-category with only identity 2-morphisms). I believe this biadjunction should restrict to a biequivalence on the sub-2-category of Tannakian categories (as you have defined them).

http://front.math.ucdavis.edu/0911.0977"" rel=""nofollow"">this paper by Daniel Schäppi (particularly the opening section), and Collin Bleak proved that $V$ does not contain subgroups isomorphic to ${\mathbb Z}^2\ast {\mathbb Z}$. Does $B_n$ contain such subgroups?

http://front.math.ucdavis.edu/0911.3599"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/0911.3599"" rel=""nofollow""> http://front.math.ucdavis.edu/0911.3599.

http://front.math.ucdavis.edu/0911.3599

http://front.math.ucdavis.edu/0911.4941"" rel=""nofollow"">nice recent preprint which, among other things, discusses a class of rings (of prime characteristic) for which a certain supersubclass of the radical ideals is closed under sum. They're called ""Frobenius split rings."" I guess they're originally defined by Brion and Kumar. They are defined to be those rings $R$ of characteristic $p$ admitting an additive map $\phi\colon R \rightarrow R$ such that $\phi(a^pb) = a\phi(b)$ and $\phi(1)=1$. An ideal $I$ is ""compatibly split"" if $\phi(I) \subseteq I$. Compatibly split ideals are radical, prime components of a compatibly split ideal are compatibly split, and if $I$ and $J$ are compatibly split, then so is $I+J$.

http://front.math.ucdavis.edu/0911.4941""> http://front.math.ucdavis.edu/0911.4941

http://front.math.ucdavis.edu/0911.4979"" rel=""noreferrer"">this paper by Justin Greenough, which more or less establishes this result in the case of sufficiently nice $k$-linear monoidal categories. But his proof seems to be very specific to that setting, whereas one would hope that a proof could be established along the same lines as the result for usual profunctors.)

http://front.math.ucdavis.edu/0912.0137"">they are biautomatic.

http://front.math.ucdavis.edu/0912.0325"" rel=""noreferrer"">Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields by Ellenberg, Venkatesh and Westerland or Terry Tao's blog entry At the AustMS conference.

http://front.math.ucdavis.edu/0912.1494"">this paper, I showed that there are subsets of size $$\gg n c^{-\sqrt{\log\log n}},$$ where $c=2^{\sqrt{8}}$, but I don't know of an upper bound.

http://front.math.ucdavis.edu/0912.2067"" rel=""nofollow"">my paper with Melvin and Mondragon.

http://front.math.ucdavis.edu/0912.3933"">arXiv. A drawback of this approach is that if you think of it as realizing some multiple $m\alpha$ of the given integral homology class $\alpha$ by an oriented smooth manifold, then $m$ is not bounded in terms of the dimension of $\alpha$.

http://front.math.ucdavis.edu/0912.4240"">alternating permutation of {1, ..., n} is one were π(1) > π(2) < π(3) > π(4) < ... For example: (24153) is an alternating permutation of length 5.

http://front.math.ucdavis.edu/0912.4706"" rel=""nofollow"">here; the fact I'm trying to prove is Lemma 2.1, which is stated without proof.

http://front.math.ucdavis.edu/0912.4914"" rel=""nofollow""> http://front.math.ucdavis.edu/0912.4914

http://front.math.ucdavis.edu/1001.2020"" rel=""nofollow"">I and Knot invariants and higher representation theory I"" and by Kang and Kashiwara in ""expository paper on Koszul duality.

http://front.math.ucdavis.edu/1001.2032"" rel=""noreferrer"">this.

http://front.math.ucdavis.edu/1001.2774"">A tropical proof of the Brill-Noether Theorem by Cools, Draisma, Payne, and Robeva. The original proof of this theorem (by Griffiths and Harris) involves subtle transversality arguments, which they are able to circumvent in this ""combinatorial"" proof. The new proof is also valid in all characteristics.

http://front.math.ucdavis.edu/1001.2949"" rel=""nofollow"">preprint which might be of interest.

http://front.math.ucdavis.edu/1001.3988"" rel=""noreferrer""> http://front.math.ucdavis.edu/1001.3988 for the essential dimension of group schemes. When $G$ is smooth over $k$, then it is easy to see that the action extends to an action on $\mathbb{P}^1$, so $G$ must be a subgroup of ${\rm PGL}_{2,k}$; but when $G$ is not smooth it is not all clear to us that this must happen. The sheaf of automorphisms of $k(t)$ over $k$ is enormous in positive characteristic, and we find it very hard to see what group schemes it contains.

http://front.math.ucdavis.edu/1001.4856"">preprint by Hofmann and Russo. There is much more besides in this preprint, I'm still digesting it myself!

http://front.math.ucdavis.edu/1002.0243"" rel=""nofollow"">this paper and its reference for this sort of thing.

http://front.math.ucdavis.edu/1002.0243"" rel=""noreferrer"">Finsler surfaces with prescribed geodesics by Gautier Berck and myself.

http://front.math.ucdavis.edu/1002.2899"" rel=""nofollow"">here and paper by LeBrun and Mason, they refer to a result by Guillemin 1976 according to which for any odd smooth function $f:S^2\to \mathbb{R}$, there is a one-parameter family $g_t=\exp(f_t)g_0$ of smooth Zoll metrics with $g_0$ the round one and $(df_t/dt)_{t=0}=f$.

http://front.math.ucdavis.edu/1002.3652"" rel=""nofollow noreferrer"">this paper.

http://front.math.ucdavis.edu/1003.0318""> http://front.math.ucdavis.edu/1003.0318

http://front.math.ucdavis.edu/1003.1568"" rel=""nofollow noreferrer"">The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link. Alexei Oblomkov, Vivek Shende. http://front.math.ucdavis.edu/1003.1805"" rel=""noreferrer"">Chamber Structure of Double Hurwitz numbers, written together with Renzo Cavalieri and Hannah Markwig, are very nice and have a lot of explicit formulas.

http://front.math.ucdavis.edu/1003.3053"" rel=""nofollow""> http://front.math.ucdavis.edu/1003.3053 for an expository article on this issue). For small systems you often get symmetry, but in large systems defects can actually lower energy in surprising ways.

http://front.math.ucdavis.edu/1003.5176"" rel=""nofollow noreferrer"">note. Possibly I missed something because I do not work in this http://front.math.ucdavis.edu/1003.5811"" rel=""nofollow"">here and his earlier paper your paper with Noah and Frank Calegari) to determine some nontrivial lower bounds on Frobenius-Perron dimensions of simple objects in $\mathcal{D}$, and thus improve on the global dimension bound.

http://front.math.ucdavis.edu/1004.1067"" rel=""nofollow"">here. In particular, under a weak form of the Elliot-Halberstam conjecture there is an integer $d>0$ such that there are arbitrary long arithmetic progressions of primes $p$ such that $p+d$ is the next prime. Assuming the full conjecture one can take $d\leq 16$, while under a natural strengthening of it one can take any even number $d>0$.

http://front.math.ucdavis.edu/1005.0353""> http://front.math.ucdavis.edu/1005.0353

http://front.math.ucdavis.edu/1005.0614"" rel=""nofollow"">here), but is a very current project, there's Lazic's proof of the finite generation of (log) canonical rings. I don't know of any great insights gained from the new proof, other than the surprising fact that it's POSSIBLE to prove it this way, and that the method, rather than requiring the Mori program to prove the theorem, allows a proof of many important theorems in the Mori program from it. This is, though, quite a work in progress.

http://front.math.ucdavis.edu/1005.0831"" rel=""nofollow""> http://front.math.ucdavis.edu/1005.0831

http://front.math.ucdavis.edu/1005.1114"" rel=""nofollow"">preprint. But it's probably most useful to contact him directly at Stanford. While the fundamental representations are obviously easier to study in many respects, it's essential to formulate your question as precisely as possible.

http://front.math.ucdavis.edu/1005.1114"" rel=""noreferrer"">here.

http://front.math.ucdavis.edu/1005.1765"">dynamics of diffeomorphisms with relation to the diffeomorphism group. There is a huge literature on the dynamics of individual diffeomorphisms, but I think this is orthogonal to your question.

http://front.math.ucdavis.edu/1005.4559"" rel=""nofollow"">II. The upshot is that there is a bilinear form on a tensor product for which the R-matrix is an isometry.

http://front.math.ucdavis.edu/1005.4559"" rel=""nofollow"">KI-HRT II; it isn't stated explicitly (I'm writing up a separate canonical basis paper at the moment), but it only requires a small twist on the current arguments. http://front.math.ucdavis.edu/1005.5056"" rel=""nofollow""> http://front.math.ucdavis.edu/1005.5056.

http://front.math.ucdavis.edu/1005.5061"" rel=""noreferrer"">McCullough and Soma have dealt many small (non-Haken) Seifert-fibered spaces. However, the case of the generalized Smale conjecture for elliptic manifolds is still open (see however the work of Hong et. al.). I think this is an important open question, and it would be useful to have a unified proof of these results (in particular, Gabai's results makes use of a http://front.math.ucdavis.edu/1006.1939 recently constructed a finite index subgroup $B$ of $G$ such that for every essential closed simple curve $\gamma$ on $S_{g}$ and every $h\in B$ either $h\gamma=\gamma$ or $h\gamma$ intersects $\gamma$ (everything is modulo isotopy of $S_{g}$). The construction is not difficult: $B$ is just the subgroup of $G$ fixing $\pi_1(S_{g})/N$ for some characteristic subgroup $N$ of the $\pi_1$ of finite index. The $N$ can be found by intersecting kernels of the first homology mod $6$ with kernels of the first homology mod 2 of all index 2 subgroups of the $\pi_1$. Question: can one find another finite index subgroup $B'$ of $G$ with the same property but with a smaller index. Most probably $B'$ cannot be above Torelli subgroup, but can it be ""not far from Torelli"". I am interested in $B'$ that does not act non-trivially on a simplicial tree. The motivation is here: http://front.math.ucdavis.edu/1006.5612 is a starting point...

http://front.math.ucdavis.edu/1007.0052"">Ranks of elliptic curves http://front.math.ucdavis.edu/1007.1998"" rel=""nofollow"">Sabalka and Savchuk to be non-hyperbolic, by showing that it contains quasiflats of arbitrarily high dimension. There is an analogue to this in Schleimer's proof that the separating curve complex of a surface is not hyperbolic, again with flats but not of arbitrarily high dimension.

http://front.math.ucdavis.edu/1007.2777"" rel=""nofollow noreferrer"">arXiv:1007.2777 includes a ""cohomological"" construction http://front.math.ucdavis.edu/1007.2777"" rel=""nofollow noreferrer"">here.

http://front.math.ucdavis.edu/1007.3146"">studied by Giesen and Topping.

http://front.math.ucdavis.edu/1007.3517"" rel=""nofollow"">Khovanov, to get an idea of what it should look like.

http://front.math.ucdavis.edu/1007.4105"" rel=""nofollow"">Kashiwara has developed some crystal theoretic methods for the Lie superalgebra $\mathfrak{q}(n)$. However, I think you should look at this paper of Berenstein and Greenstein useful, but it (and Kac's book, which it references) only deal with the finite type case. http://front.math.ucdavis.edu/1007.4357"" rel=""nofollow"">Berenstein and Greenstein in the finite case. I'm not sure if anyone has thought about the affine case.

http://front.math.ucdavis.edu/1008.0916"" rel=""noreferrer"">Aitchison.

http://front.math.ucdavis.edu/1008.1217"">here. (The intrinsic nature of the Jordan decomposition involves good behavior under linear representations. Leaving that aside, parabolic subalgebras of a given semisimple Lie algebra do contain ""semisimple"" and ""nilpotent"" elements relative to the big algebra but not relative to their own representations taken in isolation.)

http://front.math.ucdavis.edu/1008.1462"">arXiv:1008.1462.

http://front.math.ucdavis.edu/1008.3202""> http://front.math.ucdavis.edu/1008.3202 and http://front.math.ucdavis.edu/1008.3204. These papers concern statistical properties of the number of summands when writing an integer as a sum of nonconsecutive Fibonacci numbers, and generalizations to other sequences of numbers. All but one of the authors of these papers were undergraduates when they wrote the papers.

http://front.math.ucdavis.edu/1008.3868"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/1008.3868"" rel=""nofollow noreferrer"">this paper.

http://front.math.ucdavis.edu/1008.3868"" rel=""nofollow""> http://front.math.ucdavis.edu/1008.3868 .

http://front.math.ucdavis.edu/1008.3868, we show (Lemma 3.7) that for $k<2^{\lambda-1}$, the minimal $c$ is $k$. The question is what happens for $k\ge 2^{\lambda-1}$.

http://front.math.ucdavis.edu/1008.5085"" rel=""noreferrer"">this paper and this paper.

http://front.math.ucdavis.edu/1009.3188"" rel=""nofollow"">here, with a related paper http://front.math.ucdavis.edu/1009.3295 khovanov gives a nice presentation of the DAHA via a graphical calculus. The generators are then certain diagrams, and computations become somewhat more manageable (at least psychologically)

http://front.math.ucdavis.edu/1009.3869"" rel=""nofollow"">here and its references. (However, the Brown-Goodwin results might not apply directly to your situation, due to their restrictive assumption on the nilpotent orbit.)

http://front.math.ucdavis.edu/1009.3998"" rel=""nofollow noreferrer"">Tao Green and Ziegler on Gower's norms, where they look for patterns in the primes by correlating with various sequences mod 1. $\leftarrow$ If you can help me understand that paper would be nice http://front.math.ucdavis.edu/1009.5025"" rel=""nofollow"">arxiv 1009.5025 (more recent version available here). See Section 8 and figures therein. In the notation of that paper, your operad corresponds to case where all the manifolds $M_i$ and $N_i$ are $n$-cubes and all the homeomorphisms $f_i$ are the identity.

http://front.math.ucdavis.edu/1009.5025"" rel=""nofollow"">this paper). Define an $n$-category to be collection of functors on $k$-balls and homeomorphisms, for $k\le n$. The pivotal structure comes from the actions of Homeo($B^k$).

http://front.math.ucdavis.edu/1010.0548"" rel=""nofollow"">arXiv: 1010.0548 or arXiv

http://front.math.ucdavis.edu/1010.3211"" rel=""nofollow""> http://front.math.ucdavis.edu/1010.3211) use this method to proof Goettsche's conjecture about counting singular members of linear systems on surfaces. The basic idea is to write the counting problem as an intersection product of class on $S \times S^{[n]}$ and use results of Ellingsrud-Goettsche-Lehn (building on work of Nakajima) which describe the intersection theory on $S^{[n]}$.

http://front.math.ucdavis.edu/1010.5722"" rel=""nofollow""> http://front.math.ucdavis.edu/1010.5722 , which contains a lot of interesting material on similar questions).

http://front.math.ucdavis.edu/1011.0021"" rel=""nofollow"">Biringer-Johnson-Minsky prove that a power of $\psi$ extends over a compression body inside of $H_2$. This does not necessarily imply that the manifolds $M_{\psi^n}$ is not hyperbolic, but if they are I'm not sure how fast the volume grows; I suspect it would still grow linearly if some power does not extend entirely over $H_1$ or $H_2$ (like in the answer to Question 1).

http://front.math.ucdavis.edu/1011.0104"" rel=""noreferrer"">Sanders' paper.

http://front.math.ucdavis.edu/1011.5266"" rel=""noreferrer""> http://front.math.ucdavis.edu/1011.5266, http://front.math.ucdavis.edu/1011.5553"" rel=""nofollow"">the square of any 3-connected graph is 3-connected.) http://front.math.ucdavis.edu/1012.1032"" rel=""nofollow""> http://front.math.ucdavis.edu/1012.1032. In particular, it's easy to give examples where the growth rate is linear, although I'm sure there are also more elementary constructions.

http://front.math.ucdavis.edu/1012.1325"" rel=""nofollow noreferrer"">""Asymptotic invariants, complexity of groups and related problems"" for more recent examples. These include results about complexity of the word problem. Even more recent results are in papers by Olshanskii and myself (see the arXiv).

http://front.math.ucdavis.edu/1012.3643"" rel=""nofollow"">this paper of Lizhen Qin.

http://front.math.ucdavis.edu/1012.3643"" rel=""noreferrer""> http://front.math.ucdavis.edu/1012.3643

http://front.math.ucdavis.edu/1012.5636"" rel=""nofollow noreferrer"">our paper (""Alexandrov meets Kirszbraun"" by Alexander, Kapovitch and me).

http://front.math.ucdavis.edu/1012.5801"" rel=""nofollow""> http://front.math.ucdavis.edu/1012.5801 completely solves the equation $x^3+y^3=f^3+g^3$, where
http://front.math.ucdavis.edu/1101.0778"" rel=""nofollow"">Burghelea & co and arXiv: 1101.0778. Burghelea has an alternate and much simpler argument for Lizhen Qin's result, and the paper arXiv: 1101.0778 is much more readable than Qin's.

http://front.math.ucdavis.edu/1101.1810"" rel=""nofollow""> http://front.math.ucdavis.edu/1101.1810 by Elie Aidekon, which provides complete answers to your question under minimal assumptions on the jump distribution. The main result is then that $M_k - ck + (3/2) \log k$ converges to a random variable, where $c$ is a constant that is easy to compute. The distribution of the limiting random variable doesn't have to be either Gumbel or lognormal.

http://front.math.ucdavis.edu/1102.0417"" rel=""nofollow noreferrer"">Intersection patterns of convex sets via simplicial complexes, a survey.

http://front.math.ucdavis.edu/1102.0758"" rel=""noreferrer"">a preprint of Conant, Schneiderman, and Teichner. Therefore, this question might well be hopelessly naïve (it's also possible that it's open).

http://front.math.ucdavis.edu/1102.2838"" rel=""noreferrer""> http://front.math.ucdavis.edu/1102.2838

http://front.math.ucdavis.edu/1102.3234"" rel=""nofollow""> http://front.math.ucdavis.edu/1102.3234

http://front.math.ucdavis.edu/1102.3519"">here, but there are many related papers by other people including Meinolf Geck and his collaborators.

http://front.math.ucdavis.edu/1102.4677"" rel=""nofollow"">Categorification of Highest Weight Modules via Khovanov-Lauda-Rouquier Algebras.""

http://front.math.ucdavis.edu/1103.1896"">arXiv:1103.1896, in which we study the relationship between knotted trivalent graphs and Drinfel'd associators.

http://front.math.ucdavis.edu/1103.2764"" rel=""noreferrer""> http://front.math.ucdavis.edu/1103.2764. In that case, one must use fibrant approximation, and it matters what model structure one uses. When dealing with commutative ring spectra, one must use the positive stable model structure, and then one cannot just take the zeroth space. In the noncommutative case, one can use the stable model structure and then take $\Omega^{\infty}$ to mean the zeroth space of a fibrant approximation. http://front.math.ucdavis.edu/1103.3873"" rel=""nofollow"">Remark 5.23 of Sapir's paper, which attributes this as a question to Denis Osin.

http://front.math.ucdavis.edu/1103.4991"" rel=""noreferrer"">On (not) computing the Mobius function using bounded depth circuits. (See Green's answer below.)

http://front.math.ucdavis.edu/1103.5020"">here.

http://front.math.ucdavis.edu/1103.5628"" rel=""nofollow"">Chmutov, Duzhin, Mostovoy survey on the arXiv. On page 92 they have the first ten non-trivial Vassiliev invariants, computed on sufficiently-many knots. If what you're looking for isn't near there, they likely have a reference for it.

http://front.math.ucdavis.edu/1104.0749"" rel=""nofollow"">Gibbs/Metropolis algorithms on a convex polytope ... but these very complicated. Just remember the phrase ""detailed-balance"".

http://front.math.ucdavis.edu/1104.0914"" rel=""noreferrer"">Limit theory for point processes in manifolds.

http://front.math.ucdavis.edu/1104.1476"" rel=""noreferrer"">this paper.

http://front.math.ucdavis.edu/1104.1861"" rel=""nofollow noreferrer"">preprint, the factorial and $\mathbb Q$-factorial property are proved to be open for varieties over any algebraically closed field.

http://front.math.ucdavis.edu/1104.1882"" rel=""noreferrer"">upper bound on the number of Reidemeister moves, which is a tower of exponentials. The existence of some such bound is not surprising, since Waldhausen had proven that the knot isotopy problem was solvable, so some computable upper bound exists.

http://front.math.ucdavis.edu/1104.2000"" rel=""noreferrer"">Schwede-Tucker, Here is a link to the paper.

http://front.math.ucdavis.edu/1104.2632"" rel=""nofollow"">this arXiv preprint (with Z. Wang). (In the latter paper we use cubes instead of simplices to make computer implementation easier.) There's also a summary in the notes from a talk.

http://front.math.ucdavis.edu/1104.2922"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/1104.2922.)

http://front.math.ucdavis.edu/1104.4814"" rel=""nofollow"">""telescopic"" actions now. http://front.math.ucdavis.edu/1105.4597"" rel=""nofollow noreferrer"">recent paper of Hamkins, Linetsky, and Reitz is devoted to such "pointwise definable" models.

http://front.math.ucdavis.edu/1105.5955"" rel=""nofollow noreferrer"">Kapovitch--Wilking, ""Structure of fundamental groups...""). This proof would use only one result in diff-geometry: Bishop--Gromov inequality.

http://front.math.ucdavis.edu/1106.3249"" rel=""nofollow"">here. Beware of the tricky nature of sequential colimits, as noticed by Taras Banakh, The topological structure of direct limits in the category of uniform spaces.

http://front.math.ucdavis.edu/1106.3736"">""Sweeping out sectional curvature"".

http://front.math.ucdavis.edu/1107.0146"" rel=""nofollow"">Shan-Varagnolo-Vasserot. This technique doesn't have much hope of generalizing to other types (except maybe G(r,p,n)).

http://front.math.ucdavis.edu/1107.3055"" rel=""nofollow"">here.

http://front.math.ucdavis.edu/1107.3308"" rel=""nofollow"">Bestvina and Feighn. http://front.math.ucdavis.edu/1107.4717"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/1107.4717

http://front.math.ucdavis.edu/1107.5527"" rel=""noreferrer""> http://front.math.ucdavis.edu/1107.5527

http://front.math.ucdavis.edu/1107.5855"" rel=""noreferrer"">Yi Liu has proven that every closed orientable 3-manifold has a degree one map to finitely many other closed orientable 3-manifolds. I think it ought to be possible to make the proof into an algorithm. So given a closed manifold $M$, there should be an algorithm which produces finitely many manifolds $N$ such that there is a degree one map $M\to N$. It might also be possible to say something about the homotopy classes of such maps, but this hasn't been worked out. I should say also that there are many known 3-manifolds which have non-zero degree maps only to themselves or $S^3$.

http://front.math.ucdavis.edu/1108.1413"" rel=""nofollow noreferrer"">Split Metaplectic Groups and their L-groups. I think this will probably not be widely read due to the excessive use of Hopf algebras and reliance on Lusztig's canonical bases. Fortunately, I've recently worked out ways to avoid these completely, and I will hopefully have another preprint up soon.

http://front.math.ucdavis.edu/1108.2977"" rel=""noreferrer"">preprint by Dubi Kelmer, which shows among other things, that the length spectrum determines the laplace spectrum (hence the volume) for compact hyperbolic manifolds (real, complex, quaternionic or octonionic). http://front.math.ucdavis.edu/1108.3165"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/1108.3165). But it turned out to be not quite the case, although see https://reader.elsevier.com/reader/sd/pii/S0021869312003948?token=A2C6CEC757E09BD6007592434305B3AF92E3F0B70EEB14DE94288E87A2EF982C701488F77D38EE558ECF82B0039951A3. The idea of using various dimension growth functions is still alive though. See, for example, https://www.sciencedirect.com/science/article/pii/S0166864114000959

http://front.math.ucdavis.edu/1108.4708"" rel=""nofollow"">Tadashi Ochiai, Kazuma Shimomoto

http://front.math.ucdavis.edu/1108.5748"">Lemma A.6 in the Appendix of this paper, so what follows below is an outline.

http://front.math.ucdavis.edu/1109.0346"" rel=""nofollow noreferrer"">exists some kind of an infinite-dimensional extension of PL topology, which includes mapping spaces and infinite homotopy colimits up to homotopy equivalence (and hopefully up to uniform homotopy equivalence, which would be more appropriate in that setup). http://front.math.ucdavis.edu/1109.4253"" rel=""nofollow"">Contact geometry and isosystolic inequalities and the references therein) that an optimist may harbor some hope of its validity.

http://front.math.ucdavis.edu/1109.4253"">paper, but beware, by a recent preprint with Florent Balacheff, I studied a parametric version of this problem. The results suggest that the formulation above is the right way to bet. http://front.math.ucdavis.edu/1109.4253"">this paper, we guessed that the ""right"" result should be the following:

http://front.math.ucdavis.edu/1110.0228"" rel=""nofollow"">here. The earliest work tends to rely just on finite group techniques, but by now it's natural to think also about algebraic groups and to deal with general groups of Lie type. There are of course some special features of your groups which might make things easier, but it's a good idea to have the general picture in mind. (For the algebraic groups, the possible non-existence of Levi factors will be one related theme.)

http://front.math.ucdavis.edu/1110.3650"" rel=""noreferrer""> http://front.math.ucdavis.edu/1110.3650 and http://front.math.ucdavis.edu/1110.5008. Here the geometric input is minimal (namely, the Bishop-Gromov volume comparison which gives a packing condition on the orbit of the fundamental group action in the universal cover).

http://front.math.ucdavis.edu/1110.5542"">this paper or these slides) by just labeling the regions between strands as one usually does in the graphical calculus for bicategories.

http://front.math.ucdavis.edu/1110.5656"" rel=""nofollow"">highly concentrated around its mean.

http://front.math.ucdavis.edu/1110.6374"">""Pinched smooth hyperbolization"".

http://front.math.ucdavis.edu/1111.0979"" rel=""noreferrer"">this paper shows that http://front.math.ucdavis.edu/1111.1552"">13/2 ways to count curves

http://front.math.ucdavis.edu/1111.4028"" rel=""nofollow""> http://front.math.ucdavis.edu/1111.4028 Katharine Turner and I were needing this for some work on harmonic maps, and the form of the statement we prove there is below. It seems like something that would be known to folks working in this area, but we couldn't find a reference.

http://front.math.ucdavis.edu/1111.4338"" rel=""nofollow noreferrer"">this and this answers your second question positively.

http://front.math.ucdavis.edu/1111.4475"" rel=""nofollow"">arXiv:1111.4475

http://front.math.ucdavis.edu/1112.2434"">here.)

http://front.math.ucdavis.edu/1112.3932"" rel=""nofollow""> Lipshitz-Sarkar on constructing a spectrum whose (singular) homology is Khovanov homology.

http://front.math.ucdavis.edu/1112.4495"" rel=""nofollow"">preprint says that the number of commensurability classes of arithmetic lattices with a bounded number of ends is finite. Let's try to see how this might be related to your question.

http://front.math.ucdavis.edu/1112.4910"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/1112.4910.

http://front.math.ucdavis.edu/1112.5213"" rel=""nofollow"">its successor.

http://front.math.ucdavis.edu/1201.4494"" rel=""nofollow""> http://front.math.ucdavis.edu/1201.4494 http://front.math.ucdavis.edu/1202.3553"" rel=""nofollow"">Questions 2.6 and 2.9 in this paper of Constantino, Geer, and Patureau-Murand.

http://front.math.ucdavis.edu/1202.4396"" rel=""nofollow"">Noah's latest preprint with Pinhas Grossman). So the Frobenius-Perron dimensions of elements of $N \otimes_C M$ (which do not depend on knowing $D$) will give Frobenius-Perron dimensions of elements of $D$. Then I think you may be able to use the known possible small Frobenius-Perron dimensions of objects (from recover Auslander's Theorem 3 from the speech cited above (which is about support of Tor). I am optimistic that his final paragraph can be deciphered in the near future.

http://front.math.ucdavis.edu/1202.5799"" rel=""noreferrer""> http://front.math.ucdavis.edu/1202.5799 ) may as usual give that ""old meager sets are cofinal"" is the same as ""old non-meager sets are non-meager and old reals are dominating""

http://front.math.ucdavis.edu/1203.1901"">The Real Chevalley Involution (arXiv:1203:1901), page 4.

http://front.math.ucdavis.edu/1203.2260"" rel=""nofollow noreferrer""> ""algebraic"" version by Balasz Szegedy) there seem to be two versions of Fourier analysis floating around:

http://front.math.ucdavis.edu/1203.5413""> http://front.math.ucdavis.edu/1203.5413

http://front.math.ucdavis.edu/1203.5649"" rel=""noreferrer"">arXiv: 1203.5649 and the references therein. It involves some noncommutative geometry because the symbols in the Boutet-de-Monvel calculus of elliptic boundary value problems define elements in the $K$-theory of a noncommutative $C^*$-algebra. In the case of closed manifolds symbols of elliptic operators lead to elements in the $K$-theory of a commutative $C^*$-algebra.

http://front.math.ucdavis.edu/1204.1543"" rel=""nofollow"">this paper. However, it seems to me that Mazur's original formulation suggests another possible direction in which to generalize Busemann's theorem:

http://front.math.ucdavis.edu/1204.1543""> http://front.math.ucdavis.edu/1204.1543 http://front.math.ucdavis.edu/1204.2011"" rel=""nofollow""> http://front.math.ucdavis.edu/1204.2011 for a description when $d = 1$; it is clear how to generalize the formula to higher dimensions). However, one can think of $H(t)$ as a parametrized family of ""biased"" diffusion operators, i.e., a family of ""combinatorial Laplacians"" which is based on modifying the standard inner product structures on $C_{d}(X;\Bbb R)$ and $C_{d-1}(X;\Bbb R)$ using $E$ and $W$ in a suitable way.

http://front.math.ucdavis.edu/1204.3578"">Friedl and Vidussi to study http://front.math.ucdavis.edu/1204.6456"">twisted Alexander polynomials http://front.math.ucdavis.edu/1204.6474"" rel=""noreferrer""> http://front.math.ucdavis.edu/1204.6474

http://front.math.ucdavis.edu/1204.6506"">this paper:

http://front.math.ucdavis.edu/1205.0825"">other consequences besides the Willmore conjecture.

http://front.math.ucdavis.edu/1205.4577"" rel=""noreferrer"">Blickle-Schwede, easily.

http://front.math.ucdavis.edu/1205.4757"" rel=""noreferrer"">I wrote a short group theory note generalizing the 5/8 bound using a tiny bit of TQFT (itself based on an MO question).

http://front.math.ucdavis.edu/1205.6742"">Przytycki and Wise have proved that http://front.math.ucdavis.edu/1206.0490"" rel=""nofollow noreferrer"">Ershov's survey on Golod-Shafarevich groups is excellent. Highly recommended. It is published as Ershov, Mikhail Golod-Shafarevich groups: a survey. Internat. J. Algebra Comput. 22 (2012), no. 5, 1230001, 68 pp

http://front.math.ucdavis.edu/1206.1196"">homomorphisms between diffeomorphism groups for different manifolds.

http://front.math.ucdavis.edu/1206.1814"" rel=""nofollow"">Bing-Long Chen, Guoyi Xu, Zhuhong Zhang, Local pinching estimates in 3-dim Ricci flow.)

http://front.math.ucdavis.edu/1206.2635"">paper proving Theorem 5 appeared on the Arxiv recently.

http://front.math.ucdavis.edu/1206.2764"">A characterization of categories of coherent sheaves of certain algebraic stacks. In this paper, Schäppi defines the notion of a weakly Tannakian category, and shows that weakly Tannakian categories are precisely the categories of coherent sheaves for ""coherent algebraic stacks with the resolution property."" This result specializes to the classical recognition result on affine algebraic groups.

http://front.math.ucdavis.edu/1206.3626"" rel=""nofollow"">Kapovich and Rafi exploited the first of these maps to give a new proof of hyperbolicity of the free factor complex, deriving it from hyperblicity of the free splitting complex. Mann subsequently used the same method in proving hyperbolicity of the cyclic splitting complex.

http://front.math.ucdavis.edu/1207.3459"" rel=""nofollow""> http://front.math.ucdavis.edu/1207.3459""> http://front.math.ucdavis.edu/1207.3459). http://front.math.ucdavis.edu/1207.3459

http://front.math.ucdavis.edu/1207.3497"" rel=""nofollow"">Yuji Tachikawa, I found a q-deformed ""2d Yang-Mills paritition function for a cylinder"". Here it is (adapted):

http://front.math.ucdavis.edu/1207.4045"" rel=""nofollow noreferrer"">one such paper. I also created a separate route on my own website. Since then the conjectures have received several attention as you can see at these coordinates where I keep updating new papers proving the claims or certain partial progress. That is one possible choice though, you may still opt to find a home for your work in some journals, such as in Experimental Mathematics as Carlo Beenakker pointed out. Perhaps otheres can name the journals they like suggesting.

http://front.math.ucdavis.edu/1207.6321"" rel=""nofollow noreferrer"">Renormalization and Mellin transforms http://front.math.ucdavis.edu/1208.4326"" rel=""nofollow"">here.

http://front.math.ucdavis.edu/1208.5957"" rel=""noreferrer""> http://front.math.ucdavis.edu/1208.5957), but the Fukaya category is a much spookier place. http://front.math.ucdavis.edu/1209.0051"" rel=""nofollow"">Canonical bases and higher representation theory to show that this will happen whenever the graded version of this $q$-Schur algebra (which you may need to believe http://front.math.ucdavis.edu/1209.2063. The question about amenability can be reformulated in a ""Ramsey form"" which, in turn, can be formulated as existence of idempotents in certain compact magmas. In any way, reading his paper may help you find what you want.

http://front.math.ucdavis.edu/1209.3345"" rel=""nofollow"">here and papers they cite; (2) counting the number of regular semisimple elements in each type of finite torus (these being parametrized by $F$-conjugacy classes in $W$), as in older work of Fleischmann-Janiszczak in J. Algebra 155 (1993). In each case one looks for answers in the form of polynomials in $q$, which might be zero for some $q$ depending on $G^F$ and in (2) also on the type of torus. Apparently approach (1) leads to nicer and more applicable results.

http://front.math.ucdavis.edu/1209.6451"">Bunke and Tamme (their work will by the way be the topic of a summer school in Freiburg in July), but this does not in itself imply any progress on the Beilinson conjectures themselves.

http://front.math.ucdavis.edu/1210.6183"" rel=""nofollow"">Hilion and Horbez reworked that proof in the language of Hatcher's sphere systems, introducing some simplifications. http://front.math.ucdavis.edu/1211.1079

http://front.math.ucdavis.edu/1211.1730"" rel=""nofollow"">Bestvina and Feighn reworked the proof again, back in the language of $F_n$ actions on trees, introducing other simplifications. A major effect of these different proofs is to exhibit different classes of reparameterized quasigeodesics in the free splitting complex. In the case of the free splitting complex, the class of quasigeodesics called ""fold paths"" is given an explicit quasigeodesic parameterization.

http://front.math.ucdavis.edu/1211.2455"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/1211.2455

http://front.math.ucdavis.edu/1211.3430"" rel=""nofollow noreferrer"">result of Bourgain that implies that there are infinitely many m-digits primes with more than a fraction $c$ of their binary digits are ones, for some $c=1/2+m^{-\rho}$, for some $\rho<1$ Having this for $c=0.9$ will cross the square root barrier. (Update based on Christian's answer: )Eric Naslund used the results about primes in intervals to prove it for $c=0.737..$.

http://front.math.ucdavis.edu/1212.0791"" rel=""nofollow noreferrer"">here.

http://front.math.ucdavis.edu/1212.2986"" rel=""nofollow"">Brian Mann. http://front.math.ucdavis.edu/1212.3380"" rel=""nofollow""> http://front.math.ucdavis.edu/1212.3380"">here.

http://front.math.ucdavis.edu/1212.3380

http://front.math.ucdavis.edu/1212.6076"" rel=""noreferrer"">Lauda, Queffelec and Rose have proven that you always get Khovanov homology out of a category when you have a categorical action of $\mathfrak{sl}(2n)$ categorifying the simple with highest weight $(2,\dots, 2, 0, \dots, 0)$. Nakajima's construction of the action of $\mathfrak{sl}(2n)$ on the cohomology of the quiver varieties for this representation has an obvious candidate for a lift to the Fukaya category: he pushes and pulls on some Lagrangian correspondences, now just think of them as Lagrangian correspondences and look at the induced functor on the Fukaya category. There's a deformation quantization version of this that really works (this preprint for submission, I started thinking in how to give nice, (even more) explicit formulas of Finsler metrics and Lagrangians on the tangent space of the $n$-sphere or projective $n$-space for which all great circles or projective lines are extremals. I came up with this construction:

http://front.math.ucdavis.edu/1301.3191"" rel=""nofollow"">recent paper by Garner and Shulman that develops the theory of bicategories enriched in a monoidal bicategory. In particular, they show that the bicategory of (certain) modules over an enriched bicategory is the free cocompletion under (certain) weighted colimits, which allows you to describe induction as a weighted colimit as in the 1-categorical setting.

http://front.math.ucdavis.edu/1301.4919"" rel=""nofollow""> http://front.math.ucdavis.edu/1301.4919 http://front.math.ucdavis.edu/1303.4197"">result of Artstein-Avidan, Ostrover, and Karasev, a positive answer to Viterbo's conjecture would also prove the Mahler conjecture (corollary: this can't be easy!).

http://front.math.ucdavis.edu/1304.2188"">surface subgroups, and groups which do not embed uniformly in Hilbert space http://front.math.ucdavis.edu/1304.4210"" rel=""nofollow"">here.

http://front.math.ucdavis.edu/1304.6974"" rel=""nofollow"">On a fat small object argument, it is proved that in a λ-combinatorial model category, every cofibrant object is a λ-filtered colimit of λ-presentable cofibrant objects, which is close to what I wanted.

http://front.math.ucdavis.edu/1305.1698"" rel=""nofollow"">proved the conjecture you're referring to (at least for symplectic cones with a ""good"" $C^*$ action), by establishing that every such symplectic resolution is a Mori dream space. For quiver varieties, I think one doesn't need to use Namikawa's results and can just think directly about variation of GIT; this won't always give flops, but it should in the context of a symplectic reduction for a flat moment map.

http://front.math.ucdavis.edu/1305.2796"" rel=""nofollow""> http://front.math.ucdavis.edu/1305.2796"">here. Similarly, the rectangular tileability problem is undecidable according to Yang's recent result

http://front.math.ucdavis.edu/1305.4104"" rel=""noreferrer"">here. He and various collaborators have posted on arXiv a number of related papers on the faces of weight polytopes. For example, a paper with Ridenour was published in 2012 in Algebras and Representation Theory; the preprint is Rouquier-Shan-Varagnolo-Vasserot and by Losev when combined with slightly older work of a paper by Stanley and Zanello. I became curious about

http://front.math.ucdavis.edu/1305.7286"" rel=""nofollow"">Rational associahedra and noncrossing partitions

http://front.math.ucdavis.edu/1306.2391"">paper on this topic as connected to this last concern. 2-manifolds in $S^3$ have the Fox re-embedding theorem. So you could hope for some nice re-embedding theorems for $3$-manifolds in $S^4$. You shouldn't expect too nice a re-embedding theorem in $S^4$, since the tool that makes Fox's theorem work is Dehn's lemma, and the analogies to Dehn's lemma in 4-manifold theory are generally not true.

http://front.math.ucdavis.edu/1306.6049"" rel=""nofollow"">this recent preprint of Pritam Ghosh.

http://front.math.ucdavis.edu/1307.2108"" rel=""nofollow"">Dahmani . His algorithm will determine conjugacy for pairs of atoroidal outer automorphisms, ie automorphisms that do not fix a non-trivial conjugacy class. Note that he uses some very heavy machinery---his solution goes via the isomorphism problem for hyperbolic groups (solved by him and Guirardel along the lines pioneered by Sela).

http://front.math.ucdavis.edu/1308.5522"" rel=""nofollow"">arXiv:1308.5522.

http://front.math.ucdavis.edu/1308.5522"" rel=""nofollow"">this paper Balacheff, Tzanev, and I conjecture that the volume of the dual cannot be less than $(n+1)/n!$. We can prove this in dimension two under the following equivalent guise:

http://front.math.ucdavis.edu/1309.5922"">Goncharov-Shen gives a good generalization of the hive model for any reductive group $ G$. They show that $n$-fold tensor product multiplicities for $ G $ are counted by positive tropical integral points of the space $ G^\vee \setminus ( G^\vee / N)^n $. When $ G = GL_m$ and $n = 3$, this gives the Hive model. When $ G = GL_m $ and $ n = 4 $, this gives the octahedron recurrence.

http://front.math.ucdavis.edu/1310.1159""> http://front.math.ucdavis.edu/1310.1159

http://front.math.ucdavis.edu/1310.3861"" rel=""nofollow"">this paper by Clay, Forester and Louwsma. In particular, all nonsolvable B-S groups contain elements with nonzero scl, see formula (1) on page 2.

http://front.math.ucdavis.edu/1311.4600"">here) shows that if $x$ is sufficiently large, there is a Zhang prime (or even a prime $p$ so that $p+k$ is prime with $k \leq 600$) between $x$ and $2x$. It follows that there is a constant $C$ so that $z_{n} \leq C \cdot 2^{n}$, which is primitive recursive. Often in analytic number theory, it's difficult to show that something happens without showing that it happens ""a lot"".

http://front.math.ucdavis.edu/1312.5910""> http://front.math.ucdavis.edu/1312.5910, defined pseudoalgebras over operads in $Cat$. A http://front.math.ucdavis.edu/1312.7450"" rel=""nofollow""> http://front.math.ucdavis.edu/1312.7450.

http://front.math.ucdavis.edu/1402.2718"" rel=""nofollow"">highly concentrated near a certain limiting convex region that depends on the concept of randomness you use. (In particular, no chaotic white-noise-like behavior.)

http://front.math.ucdavis.edu/1402.5504"" rel=""nofollow"">here, Dipendra Prasad has revisited a 1976 theorem of Kostant (Theorem 2 in the paper On Macdonald's $\eta$-function formula, the Laplacian and generalized exponents, Advances in Math. 20 (1976), no. 2, 179-212). In the setting of a simply connected compact simple Lie group, the theorem says that any finite dimensional irreducible representation has character value $0, 1$. or $-1$ at the (lift of a) Coxeter element. Here the group could equally well be a complex Lie group or algebraic group. The Coxeter elements of the Weyl group lift to the normalizer of a maximal torus and yield a single conjugacy class in the Lie group. (This and other foundational results from Kostant's 1959 paper are surveyed in a Bourbaki talk by Koszul.)

http://front.math.ucdavis.edu/1402.6280"" rel=""nofollow"">here helps to settle your basic question positively. Though the correspondence between subgroups of Lie groups and Lie algebras in the classical situation (or more generally for algebraic groups in characteristic 0) works quite well, it usually breaks down a lot in prime characteristic. But after going through all the work to classify semisimmple and then reductive algebraic groups and especially to understand their internal structure, it turns out that many aspects of the correspondence do work (most of the time) but usually with exceptions.

http://front.math.ucdavis.edu/1403.2089"" rel=""nofollow"">arXiv:1403.2089 http://front.math.ucdavis.edu/1405.6410""> http://front.math.ucdavis.edu/1405.6410

http://front.math.ucdavis.edu/1406.5015"" rel=""nofollow"">arXiv:1406.5015 which do not admit bilipschitz embeddings into $L_1$ for the same reason.

http://front.math.ucdavis.edu/1407.0601"" rel=""nofollow"">arXiv:1407.0601

http://front.math.ucdavis.edu/1408.1443"">this paper by Amir Bahman Nasseri, Gideon Schechtman, Tomasz Tkocz, and me it is shown that there is an injective, dense range, non surjective operator on $\ell_\infty$. The proof is not technically difficult but has some interest. From the theory of Tauberian operators one deduces that such an operator exists if and only if there is a dense range, injective, non surjective operator Tauberian operator (``Tauberian"" in this context just means that the second adjoint of the operator is injective) on $L_1(0,1)$. Although $L_1(0,1)^* = L_\infty(0,1)$ is isomorphic to $\ell_\infty$, the a priori equivalence is not obvious because of the lack of reflexivity, but we need only the obvious implication. The main tool for constructing the $L_1$ operator is a finite dimensional lemma proved by computer scientists. So, in some sense, the original question about operators on a non separable Banach space is connected to computer science!

http://front.math.ucdavis.edu/1408.1929"" rel=""nofollow"">follow-up paper is available on the ArXiv and contains $n$-dimensional generalizations and interesting bibliographical remarks.

http://front.math.ucdavis.edu/1408.5746"" rel=""nofollow"">this paper the above connection is compatible with the metric and, since it is also torsion free, it must be the Levi-Civita connection !

http://front.math.ucdavis.edu/1409.1169"" rel=""noreferrer"">Smith-Zhang, posted this proof on the arXiv.)

http://front.math.ucdavis.edu/1410.2637"" rel=""nofollow noreferrer"">arXiv:1410.2637.

http://front.math.ucdavis.edu/1410.7892"">this paper, which also has more precise information on the distribution of the partial sums, including real and imaginary parts.

http://front.math.ucdavis.edu/1411.3308""> http://front.math.ucdavis.edu/1411.3308). This model is based on link diagrams with a single multicrossing, with the randomness given by a choice of random permutation, which determines the heights of the arcs relative to one another. They're actually able to compute the distribution of (appropriately scaled) linking numbers on the nose with this model. I don't think that this has been done with any other model. They do some computations of some of the moments of other low order finite type invariants too.

http://front.math.ucdavis.edu/1411.5329"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/1411.5329 http://front.math.ucdavis.edu/1412.2203"" rel=""noreferrer"">Patakfalvi-Schwede-Tucker. The original result that the FPT is $\leq$ the LCT is for $p \gg 0$ is essentially due to Hara-Watanabe (except they didn't define the FPT, that was Takagi-Watanabe and Mustata-Takagi-Watanabe, see the references contained in the above articles).

http://front.math.ucdavis.edu/1504.04401"">proven for type ADE quivers. This is actually a special case of a much more general problem, called hyperkähler Kirwan surjectivity (see, for example, this paper).

http://front.math.ucdavis.edu/1504.05409"" rel=""nofollow"">Mean values of multiplicative functions over function fields the mention a proof of Halasz inequality in one of their future pre-prints. In fact here is an a proof from 1999.

http://front.math.ucdavis.edu/1505.04451"" rel=""nofollow noreferrer"">here for the figure eight knot and $n=3$.

http://front.math.ucdavis.edu/1506.07093"">on the arXiv here).

http://front.math.ucdavis.edu/1509.02300"" rel=""nofollow noreferrer"">front.math.ucdavis.edu/1509.02300.

http://front.math.ucdavis.edu/1511.00371"" rel=""nofollow"">Differentiable stratified groupoids and a de Rham theorem for inertia spaces (arXiv:1511.00371) shows that the intertia groupoid of a Lie groupoid is at least a nicely-behaved stratified space, if not a manifold. For me at least, this is a reasonable conclusion to what the above question was asking, since from this one can then think about what the space of $k$-sectors looks like. Without more information about the groupoid one is interested in I don't believe one can say much more than this.

http://front.math.ucdavis.edu/1512.02448"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/1512.02448

http://front.math.ucdavis.edu/1512.04347"">A 'relative' local Langlands Correspondence (arXiv:1512:04347).

http://front.math.ucdavis.edu/1512.06409"" rel=""nofollow noreferrer"">Feynman Amplitudes and Cosmic Galois group http://front.math.ucdavis.edu/1512.08296"" rel=""nofollow noreferrer"">Williamson-Riche for a detailed exposition.

http://front.math.ucdavis.edu/1512.08296"" rel=""nofollow""> http://front.math.ucdavis.edu/1512.08296"" rel=""nofollow"">a conjecture of Riche and Williamson to define) is Morita equivalent to a positively graded algebra. So asking for Koszulity is, as Geordie points out, actually overkill.

http://front.math.ucdavis.edu/1512.08296

http://front.math.ucdavis.edu/1602.01484""> http://front.math.ucdavis.edu/1602.01484). This model starts with a fixed embedding of some circles in some high-dimensional Hilbert space, and randomly projects these onto a 3-dimensional subspace. In principal, the moments of the linking numbers ought to be computable. This is an intriguing model because there are continuously many parameters. It's possible that by varying the initial embeddings, these models can be made to limit to other types of models. Maybe that could explain some of the universality observed experimentally and discussed in the Petaluma paper.

http://front.math.ucdavis.edu/1608.01156"" rel=""nofollow noreferrer"">Chapter 1.

http://front.math.ucdavis.edu/1608.02572"" rel=""nofollow noreferrer"">corresponds to a (closed) subgroup of the R. Thompson group $F$. For example as shown by Guba the Brin tree-like presentation of the quaternion group corresponds to a copy of the Thompson group $F_9$ (the group of piecewise linear homeomorphisms of $[0,1]$ with slopes of the form $9^k$ and break points of the derivative from $\mathbb{Z}[1/9]$).

http://front.math.ucdavis.edu/1608.02572"" rel=""nofollow noreferrer"">this paper,but the question is purely semigroup theoretic). For example, the presentation $P$ corresponds to $F$ itself.

http://front.math.ucdavis.edu/1609.05516"" rel=""nofollow"">Comparison of the Categories of Motives defined by Voevodsky and Nori (2016)"" Daniel Harrer Compares ""V. Voevodsky's geometric motives to the derived category of M. Nori's Abelian category of mixed motives by constructing a triangulated tensor functor between them.""(compatible with the Betti realizations on both sides).

http://front.math.ucdavis.edu/1611.01812"" rel=""noreferrer"">the predual of ${\rm Lip}_0(X)$ is unique.

http://front.math.ucdavis.edu/1705.03963"" rel=""nofollow noreferrer"">here. I think the moral of the story is that there are quite a few directions in Lie theory where folding plays a significant role in getting from the simply-laced case to other cases.

http://front.math.ucdavis.edu/1707.05133"" rel=""noreferrer"">(link to arXiv) http://front.math.ucdavis.edu/1708.01081"" rel=""noreferrer"">new paper on the topic has appeared, and while it does not answer your question I find the result interesting enough to be mentioned in a separate answer.

http://front.math.ucdavis.edu/1710.00550"" rel=""noreferrer"">Olshanskii proved the same statement for all $\alpha\ge 2$ (the paper will appear in the Journal of Combinatorial Algebra). On the other hand if $\alpha$ is in the isoperimetric spectrum, then $\alpha$ can be computed in time at most $2^{2^{c2^{m}}}$ for some $c>0$. If P=NP, then one can reduce the number of 2's to two and bring the upper bound to be equal to the lower bound, completing the description of the isoperimetric spectrum. But the proof in our paper (Corollary 1.4) would give two 2's also if the following seemingly weaker conjecture holds.

http://front.math.ucdavis.edu/1804.08745"" rel=""noreferrer"">this very moment.

http://front.math.ucdavis.edu/1805.07721"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/1805.07721. In particular, Spec of the $\cdot_\infty$ is isomorphic to $(G // N \times G // N_-) // T $ by Lemma 2.8 of that paper.

http://front.math.ucdavis.edu/1809.02783"" rel=""nofollow noreferrer"">Periodic solutions of Hilbert's fourth problem.

http://front.math.ucdavis.edu/1811.05501"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/1811.05501, and http://front.math.ucdavis.edu/1812.00321"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/1812.00321, http://front.math.ucdavis.edu/1812.05126"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/1812.05126.

http://front.math.ucdavis.edu/9201.5301"" rel=""nofollow noreferrer"">here and notes for how to write a toric variety in this manner.

http://front.math.ucdavis.edu/9210.5008"">The homogenous ring of a toric variety, by David Cox. Nick Proudfoot has written an http://front.math.ucdavis.edu/9301.5212"">Freedman, He and Wang, also Jun O'Hara. But there are many other knot energies out there in the literature.

http://front.math.ucdavis.edu/9301.5212) has any critical points other than the global minimum, on the space of unknots in $S^3$.

http://front.math.ucdavis.edu/9405.5205"">Seven Trees in One and the generalization in Fiore and Leinster's Objects of Categories as Complex Numbers. As with many results of this type, I learned about this from John Baez.

http://front.math.ucdavis.edu/9412.5233"" rel=""nofollow"">Lyubich and Minsky who show how to associate a hyperbolic lamination to a rational map.

http://front.math.ucdavis.edu/9504.5230"">this paper, where I also established a similar result for the volume-preserving PL pseudogroup. In the PL case, the corresponding decoration on the manifold is a piecewise constant volume form.

http://front.math.ucdavis.edu/9506.5104"" rel=""nofollow"">Dynnikov & Vesselov.

http://front.math.ucdavis.edu/9511.5007"" rel=""nofollow"">Perverse sheaves on a Loop group and Langlands' duality

http://front.math.ucdavis.edu/9511.5111"" rel=""noreferrer""> http://front.math.ucdavis.edu/9511.5111

http://front.math.ucdavis.edu/9511.5141"" rel=""nofollow"">Majid.

http://front.math.ucdavis.edu/9609.5171"" rel=""nofollow"">paper of Chari and Pressley.

http://front.math.ucdavis.edu/9609.5207"" rel=""noreferrer"">computer-aided proof of the existence of ""non-coalescable insulator families"").

http://front.math.ucdavis.edu/9612.5114"" rel=""noreferrer"">here) for which some positive multiple of the fiber class is a basic class, and the minimal genus for the homology class of $\Sigma$ in one of these exotic $K3$ surfaces would be larger than one since there would be a basic class having positive intersection with $\Sigma$.

http://front.math.ucdavis.edu/9703.5201"" rel=""nofollow"">grows logarithmically.)

http://front.math.ucdavis.edu/9703.5222"" rel=""noreferrer"">Norms on possibilities II, Rosłanowski and Shelah use creature forcings to construct many ccc $\sigma$-ideals with properties similar to those of the ideal of meager / null sets, answering a question of Kunen.

http://front.math.ucdavis.edu/9703.5224"" rel=""nofollow""> http://front.math.ucdavis.edu/9703.5224

http://front.math.ucdavis.edu/9705.5218"" rel=""nofollow""> http://front.math.ucdavis.edu/9705.5218, but there is a more expository version available in Surgery on Contact 3-Manifolds and Stein Surfaces by Ozbagci-Stipsicz.

http://front.math.ucdavis.edu/9712.5013"" rel=""noreferrer"">This paper by Agnihotri and Woodward uses a Narasimhan-Seshadri correspondence between parabolic bundles and unitary connections to determine the possible spectrum of a product of two (special) unitary matrices of known spectrum. They start with a triple of unitary matrices with product $1$, N-S relate that to bundles on $\mathbb P^1$ with parabolic structure at three points, classify those bundles as maps of the $\mathbb P^1$ into a Grassmannian, and end up at quantum Schubert calculus of Grassmannians. Maybe not the most obviously natural source of parabolic bundles, but a wonderful application.

http://front.math.ucdavis.edu/9712.5187"" rel=""nofollow noreferrer"">here. Although the motivation is original, the invariant is a special case of more standard quantum invariants defined by other people. (The same construction was also later found by three physicists, but I can't remember their names at all right now.)

http://front.math.ucdavis.edu/9712.5188"" rel=""nofollow"">result of Kuperberg. This boils down to the question of whether the space of Jacobi diagrams with an odd number of legs vanishes. As a piece of shameless self-promotion I will refer to Choosing roots of polynomials smoothly, math.CA/9801026

http://front.math.ucdavis.edu/9801.5068"" rel=""nofollow"">math.CO/9801068? This topic may be out of fashion now but I wonder if any source code is circulating. I'm doing it myself, but I always have this fear of ""reinventing the wheel"".

http://front.math.ucdavis.edu/9801.5088"" rel=""nofollow""> http://front.math.ucdavis.edu/9801.5088

http://front.math.ucdavis.edu/9801.5119"" rel=""noreferrer"">Polishchuk and Zaslow?

http://front.math.ucdavis.edu/9802.5004"" rel=""nofollow"">here). In expositions it is convenient for people to use the special linear case as the main example, but this is of course misleading as to the delicate complications in the general case which encourage the development of multiple approaches.

http://front.math.ucdavis.edu/9803.5150"" rel=""noreferrer"">here. (Note that David Khudaverdyan has a computer-aided implementation of a curve-drawing algorithm for some planar curves, see http://front.math.ucdavis.edu/9803.5150"" rel=""noreferrer"">Millson and Kapovich paper on the topic available if you do a Google search. It seems people give a lot of credit to Bill Thurston.

http://front.math.ucdavis.edu/9805.5059"" rel=""nofollow"">this paper of Drezet and Trautmann for the kind of thing that happens.

http://front.math.ucdavis.edu/9807.5016"">which is at most exponential in $n^2$.

http://front.math.ucdavis.edu/9808.5085"" rel=""nofollow""> http://front.math.ucdavis.edu/9808.5085

http://front.math.ucdavis.edu/9808.5093"" rel=""nofollow noreferrer"">ArXiv version) and http://front.math.ucdavis.edu/9808.5093"">ArXiv version.

http://front.math.ucdavis.edu/9808.5094"" rel=""noreferrer"">easy survey http://front.math.ucdavis.edu/9808.5135"" rel=""noreferrer"">paper, explaining which parts of the story are pure combinatorics.

http://front.math.ucdavis.edu/9810.5040"">here. I believe an idea like this should work and likely Mostovoy's idea works as well, but (again) this is something that needs to be written up for which there hasn't been enough time to start the project.

http://front.math.ucdavis.edu/9811.5105"" rel=""noreferrer"">this paper).

http://front.math.ucdavis.edu/9811.5162"" rel=""noreferrer"">Gervais's presentation, proven directly by Silvia Benvenuti using an ordered complex of curves or Joswig and Ziegler to be a graph of e-polytopes for e between 4 and d.

http://front.math.ucdavis.edu/9907.5072"" rel=""noreferrer""> http://front.math.ucdavis.edu/9907.5072.

http://front.math.ucdavis.edu/9908.5029""> http://front.math.ucdavis.edu/9908.5029).

http://front.math.ucdavis.edu/9908.5171"" rel=""nofollow"">previous epic.

http://front.math.ucdavis.edu/9910.5179"" rel=""nofollow"">Keller's nice expository paper, for instance. In particular, he states this result in Section 3.3 (as a theorem due to Kadeishvili, among others). It is stated there as a result about the homology of an $A_\infty$-algebra, but any differential graded algebra may be viewed as an $A_\infty$-algebra.

http://front.math.ucdavis.edu/9911.5199"" rel=""nofollow""> http://front.math.ucdavis.edu/9911.5199 and B. Fantechi: Stacks for Everybody (you will need to google this article).

http://front.math.ucdavis.edu/9911.5249"" rel=""nofollow"">Gauld's paper, section 3.

http://front.math.ucdavis.edu/9912.5012"">Tensor product multiplicities, canonical bases and totally positive varieties, that gives (many) polyhedral models for any Lie type.

http://front.math.ucdavis.edu/9912.5088"" rel=""noreferrer"">paper, establishing localization in equivariant K-theory and explaining equivariant Grothendieck-Riemann-Roch.

http://front.math.ucdavis.edu/9912.5167"" rel=""nofollow"">Dylan Thurston and I proved that the configuration space invariant using only the flat connection is proportional to the Casson invariant, for any simple Lie group as the gauge group. (The configuration space integral is known as the theta invariant, because the Feynman-Jacobi diagram is a theta.) By contrast, Casson's invariant has been interpreted by Witten as a gauge theory with a certain Lie supergroup, whose underlying Lie group is SU(2).

http://front.math.ucdavis.edu/author/B.Burton"" rel=""nofollow"">papers of Ben Burton for implementations.

http://front.math.ucdavis.edu/author/J.Porti"" rel=""nofollow noreferrer"">Joan Porti http://front.math.ucdavis.edu/author/M.Heusener"" rel=""nofollow noreferrer"">Michael Heusener http://front.math.ucdavis.edu/author/R.Steinbauer"" rel=""nofollow"">here

http://front.math.ucdavis.edu/author/W.Crawley-Boevey"" rel=""nofollow"">papers of Bill Crawley-Boevey.

http://front.math.ucdavis.edu/categories/math"">arxiv mathematics categories, e.g. math.AT, math.QA, math.CO, etc.

http://front.math.ucdavis.edu/math"">arXiv Front for a number of subject areas, using Google Reader. This is great, but there is one problem: when a new preprint is listed in several subject categories, it gets listed in several feeds, which means I have to spend more time reading through the lists of new items, and due to my slightly dysfunctional memory, I often download the same preprint twice. Is there a way to get around this problem, by somehow merging the feeds, using a different arXiv site, or using some other clever trick?

http://front.math.ucdavis.edu/math.AG/0303052"">Points rationnels et groupes fondamentaux, applications de la cohomologie $p$-adique », Astérisque 294, p. 125-146.

http://front.math.ucdavis.edu/math.AT/0502183"" rel=""nofollow"" title=""arxiv"">Rognes' transfer of Galois theory into the context of ""brave new rings"" and his conference last year, I wonder if themes discussed in Kato's article (e.g. reciprocity laws) have ""brave new variants"".

http://front.math.ucdavis.edu/math.AT/0605069"" rel=""nofollow noreferrer"">""A family of embedding spaces"" paper I show that Litherland's spinning operation (a strictly more general spinning operation than Artin or Fox spinning) can be identified with the ""connecting map"" for the Pseudo-isotopy fibration sequence of long knot embedding spaces. Another way of saying this is that the fibrations produce natural maps

http://front.math.ucdavis.edu/math.AT/0605069"" rel=""nofollow noreferrer"">here.

http://front.math.ucdavis.edu/math.AT/0607665""> http://front.math.ucdavis.edu/math.AT/0607665 of Niko Naumann.

http://front.math.ucdavis.edu/math.CA/0102084""> http://front.math.ucdavis.edu/math.CA/0102084).

http://front.math.ucdavis.edu/math.CA/0204234"">Gerd Mockenhaupt and I managed to stumble upon half of Dvir's argument, showing that a Kakeya set in finite fields could not be contained in a low-degree algebraic variety. If we had known enough about the polynomial method to make the realisation that the exact same argument also showed that a Kakeya set could not have been contained in a high-degree algebraic variety either, we would have come extremely close to recovering Dvir's result; but our thinking was not primed in this direction.) Meanwhile, Carbery, Bennet, and I discovered that heat flow methods, of all things, could be applied to solve a variant of the Euclidean Kakeya problem (though this method did appear in literature on other analytic problems, and we viewed it as the continuous version of the discrete induction-on-scales strategy of Bourgain and Wolff.) Most recently is the work of Guth, who broke through the conventional wisdom that Dvir's polynomial argument was not generalisable to the Euclidean case by making the crucial observation that algebraic topology (such as the ham sandwich theorem) served as the continuous generalisation of the discrete polynomial method, leading among other things to the recent result of Guth and Katz you mentioned earlier.

http://front.math.ucdavis.edu/math.CO/0008220"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/math.CO/0008220 for more details. Almost all tilings will cluster around the typical tiling, so this completely determines the large-scale behavior.

http://front.math.ucdavis.edu/math.CO/0008243"" rel=""nofollow noreferrer""> http://front.math.ucdavis.edu/math.CO/0008243 (reproduced below) for a picture of a random tiling. http://front.math.ucdavis.edu/math.CO/0409062"" rel=""noreferrer""> http://front.math.ucdavis.edu/math.CO/0409062. Actually, the authors (Goh and Boyer) treat the closely related Euler polynomials and say that Bernoulli polynomials ""are easily handled with the techniques in this paper."" The connection is made explicit on page 21 of http://www.math.drexel.edu/~rboyer/talks/MIT_FINAL.pdf; the limiting curve for Bernoulli polynomials is half that of Euler polynomials. Perhaps the answer to your question can be obtained from this curve.

http://front.math.ucdavis.edu/math.CO/0411341"" rel=""nofollow"">""Cluster algebras of finite type and positive symmetrizable matrices"" by Barot, Geiss and Zelevinsky we can see that positive definite quasi-Cartan matrices (defined the same as Cartan matrices but relaxing the condition of non-positivity of elements off the diagonal) actually come from positive definite Cartan matrices. That is, each positive definite quasi-Cartan matrix is equivalent to a positive definite Cartan matrix, where equivalence in the symmetric case is defined as $A\sim B$ if there is a matrix $E$ with determinant $\pm 1$ so that $A=E^TBE$. This is proved in proposition 2.9.

http://front.math.ucdavis.edu/math.GR/0211302"" rel=""nofollow""> http://front.math.ucdavis.edu/math.GR/0211302 seems related, although it asks a slightly different question.

http://front.math.ucdavis.edu/math.GT/0203192"">his Inventiones paper with D. Calegari, which you should check out if you want more examples of non-left/right-orderable groups).

http://front.math.ucdavis.edu/math.GT/0209214"">The virtual Haken conjecture: Experiments and examples. These papers are related to earlier papers on ""random groups"" of various kind, and turned out to be connected to notions of ""growth"" of groups, to properties T and $\tau$, and to be related to sieve computations (see, e.g., this paper by Kowalski).

http://front.math.ucdavis.edu/math.GT/0303034"" rel=""nofollow noreferrer"">Budney-Conant-Scannell-Sinha.

http://front.math.ucdavis.edu/math.GT/0310328"" rel=""nofollow""> http://front.math.ucdavis.edu/math.GT/0310328

http://front.math.ucdavis.edu/math.GT/0410495"">Khovanov's homology for tangles and cobordisms is one of the papers I loved back when I hated all math papers. In particular it's a paper that has a really good use of diagrams, a lot of papers use too few diagrams and suffer a lot for it.

http://front.math.ucdavis.edu/math.GT/0506523"" rel=""nofollow noreferrer"">survey paper on the topic.

http://front.math.ucdavis.edu/math.GT/0509055"" rel=""nofollow""> http://front.math.ucdavis.edu/math.GT/0509055 http://front.math.ucdavis.edu/math.GT/0511602"" rel=""nofollow"">my own paper (joint with Tomotoda Ohtsuki), where we prove this for 3-loop Jacobi diagrams. You could ask the same question about homotopy string links, where we know that Vassiliev invariants do separate homotopy string links (see this paper by Bar-Natan). http://front.math.ucdavis.edu/math.LO/0504196"" rel=""nofollow"">Sh:840). I am unfamiliar with either proof, but here is Shelah's abstract:

http://front.math.ucdavis.edu/math.LO/9205208"" rel=""nofollow noreferrer"">paper of Shelah and Goldstern devoted to the separation of many simple cardinal invariants (this is a technical term). There are more recent papers on this subject by Kellner and Shelah, if I remember correctly.

http://front.math.ucdavis.edu/math.LO/9509228"">arxiv

http://front.math.ucdavis.edu/math.LO/9809200"" rel=""nofollow noreferrer"">this paper entitled "The Generalized Continuum Hypothesis revisited "). See also the paper entitled "You can enter Cantor paradise" (Offered in Haim's answer.);

http://front.math.ucdavis.edu/math.MG/0110009"">Henry Cohn and Noam Elkies.

http://front.math.ucdavis.edu/math.MG/0403263""> http://front.math.ucdavis.edu/math.MG/0403263).

http://front.math.ucdavis.edu/math.NT/0204035"" rel=""nofollow""> http://front.math.ucdavis.edu/math.NT/0204035. The case where $t$ is truly a rational variable is more complicated. here.

http://front.math.ucdavis.edu/math.NT/0610021"">Kowalski (The principle of the large sieve):

http://front.math.ucdavis.edu/math.QA/0202258"">this arXiv paper by Etingof and Gelaki. (The theorem cited as [De2] is the relevant one.)

http://front.math.ucdavis.edu/math.QA/0301090"" rel=""nofollow"">math.QA/0301090, Banach Center Publ. 61, pp. 265--298, Warszawa 2003;

http://front.math.ucdavis.edu/math.RT/0604096"">math.RT/0604096). http://front.math.ucdavis.edu/math.SG/0502404"">arXiv: math.SG/0502404

http://front.math.ucdavis.edu/math/0012219"" rel=""nofollow"">Champs affines.

http://front.math.ucdavis.edu/math/0405366"">[arXiv:math/0405366] which suggests a method that could give you a covering radius, although in my paper it was the analytically easier case of a compact domain. The idea is to find an $f(x) = f(||x||_2)$ whose integral is positive, yet which is non-positive for $||x||_2 > c$, and whose Fourier transform satisfies the support condition. Then $\Lambda^*$ must have a lattice point in the ball $B_c(0)$, and indeed in $B_c(p)$ for any $p$. I call this the ""positive island"" method.

http://front.math.ucdavis.edu/math/0812.1407""> http://front.math.ucdavis.edu/math/0812.1407

http://front.math.ucdavis.edu/math/9201301"">arXiv:math/9201301 and http://front.math.ucdavis.edu/math/9502238

http://front.math.ucdavis.edu/math/9511224"" rel=""nofollow"">arXiv:math/9511224]) that you might as well let a Rodl nibble be just a single block. This simplifies Rodl's construction to the random greedy algorithm. There is also a non-rigorous model that correctly predicts the rate at which the random greedy http://front.math.ucdavis.edu/math/9807012"">arXiv:math/9807012], and the Hass-Lagarias-Pippenger result that unknottedness is in NP [arXiv:math/9807016]. In fact the two results are related in the converse direction. Their certificate of unknottedness is a disk which may have exponential area and gives you the moves; but the disk has a polynomial-length description.

http://front.math.ucdavis.edu/q-alg/9606016"">""Lie Algebras and the Four Color Theorem"" by Dror Bar-Natan qualify ?

http://front.math.ucdavis.edu/q-alg/9606021"" rel=""noreferrer"">arXiv:q-alg/960621, remark 2.5), but now I'm no longer sure. If the above is false, I will need to make some minor changes to said paper, but these changes are localized and nothing major changes.

http://front.math.ucdavis.edu/q-alg/9712047"">arXiv:q-alg/9712047. At the time I hadn't heard of the name ""trace diagrams"" and I called it instead ""arrow notation"", and I included a review of the notation. The diagrams are very useful for understanding word relations in Hopf algebras.

http://front.math.ucdavis.edu/search?a=&t=&q=triple+product+identity&c=&n=28"">still actively studied in many contexts.

http://front.math.ucdavis.edu/search?a=donagi&t=langlands&q=&c=&n=25&s=Listings"" rel=""nofollow"">advisor, as well as the work of Frenkel and Gaitsgory, is my understanding.

http://front.math.ucdavis.edu/search?a=gang+tian&t=&q=&c=math&n=25&s=Listings"" rel=""noreferrer"">Gang Tian.

http://front.math.ucdavis.edu/search?a=Nathanson%2C+Melvyn&t=&q=&c=&n=40&s=Listings"" rel=""nofollow""> http://front.math.ucdavis.edu/search?a=Nathanson%2C+Melvyn&t=&q=&c=&n=40&s=Listings.

http://front.math.ucdavis.edu/search?a=rosly&t=&q=polar%20homology"" rel=""nofollow"">these papers Khesin, Rosly, and later Thomas build a homology theory based on this analogy.

http://front.math.ucdavis.edu/search?a=simon+donaldson&t=&q=&c=math&n=25&s=Listings"" rel=""noreferrer"">Simon Donaldson and Witten which is closely related. To really get this, you need to have a bit of an understanding of the Hitchin system on Higgs bundles (though not by that name, they're used extensively in this paper).

http://front.math.ucdavis.edu/search?a=yagasaki&t=&q=&c=math&n=25&s=Listings""> papers of Yagasaki on arxiv https://front.math.ucdavis.edu/abs/1903.01444"" rel=""nofollow noreferrer""> https://front.math.ucdavis.edu/abs/1903.01444) that this holds for elliptic curves $E$ with normal bundle $L$ s. t. $-\log d(\mathscr{O}_E,L^{\otimes n}) = O(\log n)$ for any invariant metric $d$ on the Picard torus. This is attributed to Arnold, and should be related to his work on small denominators in celestial mechanics. The paper due to Arnold referred by Koike and Uehara lacks the proof, though.

https://front.math.ucdavis.edu/math.LO/0010070"" rel=""nofollow noreferrer"">Measured Creatures" https://front.math.ucdavis.edu/math.LO/0406612"" rel=""nofollow noreferrer"">How much sweetness is there in the universe?" https://front.math.ucdavis.edu/math.LO/0611131"" rel=""nofollow noreferrer"">Lords of the iteration" https://front.math.ucdavis.edu/math.LO/9909115"" rel=""nofollow noreferrer"">Sweet & Sour and other flavours of ccc forcing notions"