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作者：Geck, Meinolf
作者单位：University of Aberdeen
摘要：Let H be the one-parameter Hecke algebra associated to a finite Weyl group W, defined over a ground ring in which bad primes for W are invertible. Using deep properties of the Kazhdan-Lusztig basis of H and Lusztig's a-function, we show that H has a natural cellular structure in the sense of Graham and Lehrer. Thus, we obtain a general theory of Specht modules for Hecke algebras of finite type. Previously, a general cellular structure was only known to exist in types A(n) and B-n .
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作者：Kiselev, A.; Nazarov, F.; Volberg, A.
作者单位：University of Wisconsin System; University of Wisconsin Madison; Michigan State University
摘要：We give an elementary proof of the global well-posedness for the critical 2D dissipative quasi-geostrophic equation. The argument is based on a non-local maximum principle involving appropriate moduli of continuity.
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作者：Lee, Yongnam; Park, Jongil
作者单位：Sogang University; Seoul National University (SNU)
摘要：In this paper we construct a simply connected, minimal, complex surface of general type with p(g) = 0 and K-2 = 2 using a rational blow-down surgery and a Q-Gorenstein smoothing theory.
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作者：Le Gall, Jean-Francois
作者单位：Universite PSL; Ecole Normale Superieure (ENS)
摘要：We discuss scaling limits of large bipartite planar maps. If p >= 2 is a fixed integer, we consider, for every integer n >= 2, a random planar map M (n) which is uniformly distributed over the set of all rooted 2p-angulations with n faces. Then, at least along a suitable subsequence, the metric space consisting of the set of vertices of M-n , equipped with the graph distance rescaled by the factor n(-1/4), converges in distribution as n -> infinity towards a limiting random compact metric spac...
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作者：Erdos, Laszlo; Schlein, Benjamin; Yau, Horng-Tzer
作者单位：University of Munich; Harvard University
摘要：We prove rigorously that the one-particle density matrix of three dimensional interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of the cubic non-linear Schrodinger equation in a suitable scaling limit. The result is extended to k-particle density matrices for all positive integer k.
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作者：Toen, Bertrand
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：The main purpose of this work is to study the homotopy theory of dg-categories up to quasi-equivalences. Our main result is a description of the mapping spaces between two dg-categories C and D in terms of the nerve of a certain category of (C,D)-bimodules. We also prove that the homotopy category Ho(dg-Cat) possesses internal Hom's relative to the (derived) tensor product of dg-categories. We use these two results in order to prove a derived version of Morita theory, describing the morphisms ...
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作者：Gritsenko, V. A.; Hulek, K.; Sankaran, G. K.
作者单位：Universite de Lille; Leibniz University Hannover; University of Bath
摘要：The global Torelli theorem for projective K3 surfaces was first proved by Piatetskii-Shapiro and Shafarevich 35 years ago, opening the way to treating moduli problems for K3 surfaces. The moduli space of polarised K3 surfaces of degree 2d is a quasi-projective variety of dimension 19. For general d very little has been known hitherto about the Kodaira dimension of these varieties. In this paper we present an almost complete solution to this problem. Our main result says that this moduli space ...
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作者：Alvarez-Consul, Luis; King, Alastair
作者单位：Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencias Matematicas (ICMAT); University of Bath
摘要：We show how natural functors from the category of coherent sheaves on a projective scheme to categories of Kronecker modules can be used to construct moduli spaces of semistable sheaves. This construction simplifies or clarifies technical aspects of existing constructions and yields new simpler definitions of theta functions, about which more complete results can be proved.
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作者：Ni, Yi
作者单位：Princeton University
摘要：Ozsvath and Szabo conjectured that knot Floer homology detects fibred knots in S-3. We will prove this conjecture for null-homologous knots in arbitrary closed 3-manifolds. Namely, if K is a knot in a closed 3-manifold Y, Y - K is irreducible, and (HFK) over cap (Y, K) is monic, then K is fibred. The proof relies on previous works due to Gabai, Ozsvath-Szabo, Ghiggini and the author. A corollary is that if a knot in S-3 admits a lens space surgery, then the knot is fibred.
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作者：Pappas, Georgios
作者单位：Michigan State University
摘要：We show that, in characteristic zero, the obvious integral version of the Grothendieck-Riemann-Roch formula obtained by clearing the denominators of the Todd and Chern characters is true (without having to divide the Chow groups by their torsion subgroups). The proof introduces an alternative to Grothendieck's strategy: we use resolution of singularities and the weak factorization theorem for birational maps.
