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作者：Abouzaid, Mohammed
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We prove that the inclusion of every closed exact Lagrangian with vanishing Maslov class in a cotangent bundle is a homotopy equivalence. We start by adapting an idea of Fukaya-Seidel-Smith to prove that such a Lagrangian is equivalent to the zero section in the Fukaya category with integral coefficients. We then study an extension of the Fukaya category in which Lagrangians equipped with local systems of arbitrary dimension are admitted as objects, and prove that this extension is generated, ...
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作者：Ballard, Matthew; Favero, David; Katzarkov, Ludmil
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Vienna
摘要：The Orlov spectrum is a new invariant of a triangulated category. It was introduced by D. Orlov, building on work of A. Bondal-M. Van den Bergh and R. Rouquier. The supremum of the Orlov spectrum of a triangulated category is called the ultimate dimension. In this work, we study Orlov spectra of triangulated categories arising in mirror symmetry. We introduce the notion of gaps and outline their geometric significance. We provide the first large class of examples where the ultimate dimension i...
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作者：Guentner, Erik; Tessera, Romain; Yu, Guoliang
作者单位：Vanderbilt University; University of Hawaii System; University of Hawaii Manoa
摘要：We introduce a geometric invariant, called finite decomposition complexity (FDC), to study topological rigidity of manifolds. We prove for instance that if the fundamental group of a compact aspherical manifold M has FDC, and if N is homotopy equivalent to M, then Mxae (n) is homeomorphic to Nxae (n) , for n large enough. This statement is known as the stable Borel conjecture. On the other hand, we show that the class of FDC groups includes all countable subgroups of GL(n,K), for any field K.
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作者：Cadoret, Anna; Tamagawa, Akio
作者单位：Kyoto University; Centre National de la Recherche Scientifique (CNRS); Inria; Universite de Bordeaux
摘要：Let k be a field finitely generated over Q and p a prime. The torsion conjecture (resp. p-primary torsion conjecture) for abelian varieties over k predicts that the k-rational torsion (resp. the p-primary k-rational torsion) of a d-dimensional abelian variety A over k should be bounded only in terms of k and d. These conjectures are only known for d = 1. The p-primary case was proved by Y. Manin, in 1969; the general case was completed by L. Merel, in 1996, after a series of contributions by B...
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作者：Chelkak, Dmitry; Smirnov, Stanislav
作者单位：Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Scientific Centre of the Russian Academy of Sciences; Saint Petersburg State University; University of Geneva
摘要：It is widely believed that the celebrated 2D Ising model at criticality has a universal and conformally invariant scaling limit, which is used in deriving many of its properties. However, no mathematical proof has ever been given, and even physics arguments support (a priori weaker) Mobius invariance. We introduce discrete holomorphic fermions for the 2D Ising model at criticality on a large family of planar graphs. We show that on bounded domains with appropriate boundary conditions, those ha...
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作者：Zhang, Wei
作者单位：Harvard University
摘要：We present a relative trace formula approach to the Gross-Zagier formula and its generalization to higher-dimensional unitary Shimura varieties. As a crucial ingredient, we formulate a conjectural arithmetic fundamental lemma for unitary Rapoport-Zink spaces. We prove the conjecture when the Rapoport-Zink space is associated to a unitary group in two or three variables.
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作者：Oh, Hee; Shah, Nimish
作者单位：Brown University; Korea Institute for Advanced Study (KIAS); University System of Ohio; Ohio State University
摘要：Let P be a locally finite circle packing in the plane C invariant under a non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When Gamma is geometrically finite, we construct an explicit Borel measure on C which describes the asymptotic distribution of small circles in P, assuming that either the critical exponent of Gamma is strictly bigger than 1 or P does not contain an infinite bouquet of tangent circles glued at a parabolic fixed point of Gamma. Our construction also ...
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作者：Ardakov, Konstantin
作者单位：University of London
摘要：Let G be a nilpotent complete p-valued group of finite rank and let k be a field of characteristic p. We prove that every faithful prime ideal of the Iwasawa algebra kG is controlled by the centre of G, and use this to show that the prime spectrum of kG is a disjoint union of commutative strata. We also show that every prime ideal of kG is completely prime. The key ingredient in the proof is the construction of a non-commutative valuation on certain filtered simple Artinian rings.
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作者：Rolla, Leonardo T.; Sidoravicius, Vladas
作者单位：Universite PSL; Ecole Normale Superieure (ENS)
摘要：We study the long-time behavior of conservative interacting particle systems in Z: the activated random walk model for reaction-diffusion systems and the stochastic sandpile. We prove that both systems undergo an absorbing-state phase transition.
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作者：Pop, Florian
作者单位：University of Pennsylvania
摘要：Recall that a program initiated by Bogomolov in 1990 aims at reconstructing function fields K vertical bar k with td(K vertical bar k) > 1 and k algebraically closed from the maximal pro-l abelian-by-central Galois group Pi(c)(K) of K, where l is any prime number not equal char(k). In this paper we complete that program in the case k is an algebraic closure of a finite field.
