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作者：Lin, Hsueh-Yung; Shinder, Evgeny
摘要：We construct invariants of birational maps with values in the Kontsevich- Tschinkel group and in the truncated Grothendieck groups of varieties. These invariants are morphisms of groupoids and are well -suited to investigating the structure of the Grothendieck ring and L -equivalence. Building on known constructions of L -equivalence, we prove new unexpected results about Cremona groups.
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作者：Mattheus, Sam; Verstraete, Jacques
摘要：For integers s, t >= 2, the Ramsey number r(s, t) denotes the minimum n such that every n-vertex graph contains a clique of order s or an independent set of order t. In this paper we prove r(4, t) = Omega (t(3)/log(4)t) as t -> infinity, which determines r(4, t) up to a factor of order log(2)t, and solves a conjecture of Erdos.
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作者：Caraiani, Ana; Scholze, Peter
摘要：We prove that the generic part of the mod $ cohomology of Shimura varieties associated to quasi-split unitary groups of even dimension is concentrated above the middle degree, extending our previous work to a noncompact case. The result applies even to Eisenstein cohomology classes coming from the locally symmetric space of the general linear group, and has been used in joint work with Allen, Calegari, Gee, Helm, Le Hung, Newton, Taylor and Thorne to get good control on these classes and deduc...
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作者：Cristofaro-Gardiner, Daniel; Humiliere, Vincent; Seyfaddini, Sobhan
摘要：In the 1970s, Fathi, having proven that the group of compactly supported volume -preserving homeomorphisms of the n -ball is simple for n >= 3, asked if the same statement holds in dimension two. We show that the group of compactly supported area -preserving homeomorphisms of the twodisc is not simple. This settles what is known as the simplicity conjecture in the affirmative. In fact, we prove the a priori stronger statement that this group is not perfect. Our general strategy is partially in...
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作者：Bradlow, Steven; Collier, Brian; Garcia-Prada, Oscar; Gothen, Peter b.; Oliveira, Andre
摘要：We introduce a new class of sl 2-triples in a complex simple Lie algebra g , which we call magical. Such an sl 2-triple canonically defines a real form and various decompositions of g . Using this decomposition data, we explicitly parametrize special connected components of the moduli space of Higgs bundles on a compact Riemann surface X for an associated real Lie group, hence also of the corresponding character variety of representations of pi 1X in the associated real Lie group. This recover...
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作者：Fu, Weibo
摘要：We prove a degree-one saving bound for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on SL2 over any number field that is not totally real. In particular, we establish a sharp bound on the growth of cuspidal Bianchi modular forms. We transfer our problem into a question over the completed universal enveloping algebras by applying an algebraic microlocalization of Ardakov and Wadsley to the completed homology. We prove finitely generated Iwasawa...
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作者：Baldi, Gregorio; Ullmo, Emmanuel
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作者：Masmoudi, Nader; Zhao, Weiren
摘要：We prove the nonlinear inviscid damping for a class of monotone shear flows in T x [0, 1] for initial perturbation in Gevrey- 1/s class (1 < 1/s < 2) with compact support. The main new idea of the proof is to construct and use the wave operator of a slightly modified Rayleigh operator in a well-chosen coordinate system.
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作者：Allen, Patrick B.; Calegari, Frank; Caraiani, Ana; Gee, Toby; Helm, David; Le Hung, Bao V.; Newton, James; Scholze, Peter; Taylor, Richard; Thorne, Jack A.
摘要：Let F be a CM number field. We prove modularity lifting theorems for regular n-dimensional Galois representations over F without any self-duality condition. We deduce that all elliptic curves E over F are potentially mod-ular, and furthermore satisfy the Sato-Tate conjecture. As an application of a different sort, we also prove the Ramanujan Conjecture for weight zero cuspidal automorphic representations for GL2(AF).
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作者：Edelen, Nick; Spolaor, Luca
摘要：Hardt-Simon proved that every area-minimizing hypercone C having only an isolated singularity fits into a foliation of Rn+1 by smooth, areaminimizing hypersurfaces asymptotic to C. In this paper we prove that if a stationary integral n-varifold M in the unit ball B-1 subset of Rn+1 lies sufficiently close to a minimizing quadratic cone (for example, the Simons' cone C-3,C-3), then spt M boolean AND B-1/2 is a C-1,C- alpha perturbation of either the cone itself, or some leaf of its associated f...
