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作者：Burguet, David
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：AC(infinity) smooth surface diffeomorphism admits an SRB measure if and only if the set{x,lim sup(n)(1)/(n )log & Vert;d(x)f(n)& Vert;>0}has positive Lebesgue measure. Moreover the basinsof the ergodic SRB measures are covering this set Lebesgue almost everywhere. Wealso obtain similar results forCrsurface diffeomorphisms with+infinity>r>1.
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作者：Feng, Tony; Yun, Zhiwei; Zhang, Wei
作者单位：University of California System; University of California Berkeley; Massachusetts Institute of Technology (MIT)
摘要：We construct special cycles on the moduli stack of hermitian shtukas. We prove an identity between (1) the rth central derivative of non-singular Fourier coefficients of a normalized Siegel-Eisenstein series, and (2) the degree of special cycles of virtual dimension 0 on the moduli stack of hermitian shtukas with r legs. This may be viewed as a function-field analogue of the Kudla-Rapoport Conjecture, that has the additional feature of encompassing all higher derivatives of the Eisenstein seri...
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作者：Shkoller, Steve; Vicol, Vlad
作者单位：University of California System; University of California Davis; New York University
摘要：We construct a fundamental piece of the boundary of the maximal globally hyperbolic development (MGHD) of Cauchy data for the multi-dimensional compressible Euler equations, which is necessary for the local shock development problem. For an open set of compressive and generic H7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{...
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作者：Disegni, Daniel; Liu, Yifeng
作者单位：Ben-Gurion University of the Negev; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Zhejiang University
摘要：Fix a prime number p and let E/F be a CM extension of number fields in which p splits relatively. Let pi be an automorphic representation of a quasi-split unitary group of even rank with respect to E/F such that pi is ordinary above p with respect to the Siegel parabolic subgroup. We construct the cyclotomic p-adic L-function of pi, and a certain generating series of Selmer classes of special cycles on Shimura varieties. We show, under some conditions, that if the vanishing order of the p-adic...
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作者：Peluse, Sarah; Prendiville, Sean
作者单位：Stanford University; Lancaster University
摘要：We show that there exists c>0 such that any subset of {1, ... ,N} of density at least (log log N)(-c) contains a nontrivial progression of the form x, x+y, x+y(2). This is the first quantitatively effective version of the Bergelson-Leibman polynomial Szemeredi theorem for a progression involving polynomials of differing degrees. Our key innovation is an inverse theorem characterising sets for which the number of configurations x, x+y, x+y(2) deviates substantially from the expected value. In p...
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作者：Connery-Grigg, Dustin
作者单位：Sorbonne Universite
摘要：We develop connections between the qualitative dynamics of Hamiltonian isotopies on a surface Sigma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Sigma $\end{document} and their chain-level Floer theory using ideas drawn from Hofer-Wysocki-Zehnder's theory of finite energy foliations. We associate to every collect...
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作者：Louder, Larsen; Wilton, Henry
作者单位：University of London; University College London; University of Cambridge
摘要：Previously, the authors proved that the presentation complex of a one-relator group G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$G$\end{document} satisfies a geometric condition called negative immersions if every two-generator, one-relator subgroup of G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepack...
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作者：Keevash, Peter; Lifshitz, Noam; Minzer, Dor
作者单位：University of Oxford; Hebrew University of Jerusalem; Massachusetts Institute of Technology (MIT)
摘要：A subset A of a group G is called product-free if there is no solution to a = bc with a, b, c all in A. It is easy to see that the largest product-free subset of the symmetric group Sn is obtained by taking the set of all odd permutations, i.e. S-n\A(n), where A(n) is the alternating group. In 1985 Babai and Sos (Eur. J. Comb. 6(2):101-114, 1985) conjectured that the group A(n) also contains a product-free set of constant density. This conjecture was refuted by Gowers (whose result was subsequ...
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作者：Zhuang, Ziquan
作者单位：Johns Hopkins University
摘要：We show that direct summands (or more generally, pure images) of klt type singularities are of klt type. As a consequence, we give a different proof of a recent result of Braun, Greb, Langlois and Moraga that reductive quotients of klt type singularities are of klt type.
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作者：Liu, Yuan; Wood, Melanie Matchett; Zureick-Brown, David
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Harvard University; Amherst College
