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作者：Kwan, Matthew; Sah, Ashwin; Sawhney, Mehtaab; Simkin, Michael
摘要：We prove a 1973 conjecture due to Erd & odblac;s on the existence of Steiner triple systems with arbitrarily high girth.
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作者：Dolgopyat, D.; Kanigowski, A.; Hertz, F. Rodriguez
摘要：Let f be a C 1+ alpha diffeomorphism of a compact manifold M preserving a smooth measure mu . We show that if f : ( M, mu ) -> ( M, mu ) is exponentially mixing, then it is Bernoulli.
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作者：Ganatra, Sheel; Pardon, John; Shende, Vivek
摘要：The Nadler-Zaslow correspondence famously identifies the finite-dimensional Floer homology groups between Lagrangians in cotangent bundles with the finite-dimensional Hom spaces between corresponding constructible sheaves. We generalize this correspondence to incorporate the infinite-dimensional spaces of morphisms at infinity, given on the Floer side by Reeb trajectories (also known as wrapping) and on the sheaf side by allowing unbounded infinite rank sheaves which are categorically compact....
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作者：Paolini, Gianluca; Shelah, Saharon
摘要：We prove that the Borel space of torsion -free abelian groups with domain omega is Borel complete, i.e., the isomorphism relation on this Borel space is as complicated as possible, as an isomorphism relation. This solves a longstanding open problem in descriptive set theory, which dates back to the seminal paper on Borel reducibility of Friedman and Stanley from 1989.
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作者：Cai, Yuanqing; Friedberg, Solomon; Kaplan, Eyal
摘要：We study the generalized doubling method for pairs of representations of G x GLk where G is a symplectic group, split special orthogonal group or split general spin group. We analyze the poles of the local integrals and prove that the global completed L-function with a cuspidal representation of GLk twisted by a highly ramified Hecke character is entire. We obtain a new proof of the weak functorial transfer of cuspidal automorphic representations of G to the natural general linear group, which...
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作者：Lee, Yin Tat; Vempala, Santosh S.
摘要：We analyze the Poincar & eacute; and Log-Sob olev constants of logconcave densities in Rn. For the Poincar & eacute; constant, we give an improved estimate of O(root n) for any isotropic logconcave density. For the Log-Sob olev constant, we prove a bound of Omega(1/D), where D is the diameter of the support of the density, and show that this is asymptotically the best possible bound, resolving a question posed by Frieze and Kannan in 1997. These bounds have several interesting consequences. Im...
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作者：Dunn, Alexander; Radziwill, Maksym
摘要：Let W be a smooth test function with compact support in (0, oo). Conditional on the Generalized Riemann Hypothesis for Hecke L-functions over Q ( omega ), we prove that X p equivalent to 1 (mod 3) 1 ( X e 2 pi ix 3 /p ) ( p ) 2 root p WX x (mod p ) (2 pi)2/3 Z infinity ti W(x)x-1/6dx X 5 / 6 3 Gamma(23) logX, 0 as X-* oo and p runs over primes. This explains a well-known numerical bias in the distribution of cubic Gauss sums first observed by Kummer in 1846 and confirms (conditionally on the G...
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作者：Bergstrom, Jonas; Faber, Carel; Payne, Sam
摘要：We compute the number of F-q-points on (M) over bar (4,n) for n <= 3 and show that it is a polynomial in q , using a sieve based on Hasse-Weil zeta functions. As an application, we prove that the rational singular cohomology group H-k((M) over bar (g,n)) vanishes for all odd k <= 9. Both results confirm predictions of the Langlands program, via the conjectural correspondence with polarized algebraic cuspidal automorphic representations of conductor 1, which are classified in low weight. Our va...
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作者：Park, Jinyoung; Pham, Huy tuan
摘要：For appropriate Gaussian processes, as a corollary of the majorizing measure theorem, Michel Talagrand (1987) proved that the event that the supremum is significantly larger than its expectation can be covered by a set of half-spaces whose sum of measures is small. We prove a conjecture of Talagrand that is the analog of this result in the Bernoulli-p setting, and answer a question of Talagrand on the analogous result for general positive empirical processes.
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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...
