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作者：Puschnigg, M
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
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作者：Etingof, P; Ginzburg, V
作者单位：Massachusetts Institute of Technology (MIT); University of Chicago
摘要：To any finite group Gamma subset of Sp(V) of automorphisms of a symplectic vector space V we associate a new multi-parameter deformation, H-kappa of the algebra C[V]#Gamma, smash product of Gamma with the polynomial algebra on V. The parameter kappa runs over points of P-r, where r = number of conjugacy classes of symplectic reflections in Gamma. The algebra H-kappa called a symplectic reflection algebra, is related to the coordinate ring of a Poisson deformation of the quotient singularity V/...
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作者：Lafforgue, L
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay; Universite Paris Saclay
摘要：One proves Langlands' correspondence for GL, over function fields. This is a generalization of Drinfeld's proof in the case of rank 2 : Langlands' correspondence is realized in l-adic cohomology spaces of the modular varieties classifying rank r Drinfeld shtukas.
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作者：Jonsson, M; Varolin, D
作者单位：University of Michigan System; University of Michigan
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作者：Bergelson, V; Leibman, A
作者单位：University System of Ohio; Ohio State University
摘要：Let T and S be invertible measure preserving transformations of a probability measure space (X, B, mu). We prove that if the group generated by T and S is nilpotent, then lim(N-->infinity) 1/N Sigma(n=1)(N) u(T(n)x)v(S(n)x) exists in L-2-norm for any u, v epsilon L-infinity(X, B, mu). We also show that for A epsilon B with mu(A) > 0 one has lim(N-->infinity) 1/N Sigma(n=1)(N) mu(A boolean AND T-n A boolean AND S-n A) > 0. By the way of contrast, we bring examples showing that if measure preser...
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作者：Ionel, EN
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：We show that any degree at least g monomial in descendant or tautological classes vanishes on M-g,M-n when g greater than or equal to 2. This generalizes a result of Looijenga and proves a version of Getzler's conjecture. The method we use is the study of the relative Gromov-Witten invariants of P-1 relative to two points combined with the degeneration formulas of [IP1].
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作者：Cantarella, J; Kusner, RB; Sullivan, JM
作者单位：University System of Georgia; University of Georgia; University of Massachusetts System; University of Massachusetts Amherst; University of Illinois System; University of Illinois Urbana-Champaign
摘要：The ropelength of a knot is the quotient of its length by its thickness, the radius of the largest embedded normal tube around the knot. We prove existence and regularity for ropelength minimizers in any knot or link type; these are C-1,C- 1 curves, but need not be smoother. We improve the lower bound for the ropelength of a nontrivial knot, and establish new ropelength bounds for small knots and links, including some which are sharp.
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作者：Etnyre, JB; Honda, K
作者单位：University of Pennsylvania; University of Southern California
摘要：We exhibit tight contact structures on 3-manifolds that do not admit any symplectic fillings.
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作者：Sarig, O
作者单位：University of Warwick
摘要：We describe a method for proving subexponential lower bounds for correlations functions, and apply it to study decay of correlations for maps with countable Markov partitions. One result is that LS Young's upper estimates [Y2] are optimal in many situations. Our method is based on a general result concerning the asymptotics of renewal sequences of bounded operators acting on Banach spaces, which we apply to the iterates of the transfer operator.
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作者：Chambert-Loir, A; Tschinkel, Y
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Princeton University
摘要：We prove asymptotic formulas for the number of rational points of bounded height on smooth equivariant compactifications of the affine space.
