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作者：Huang, Jingyin
作者单位：University System of Ohio; Ohio State University
摘要：We show that for a large class of Artin groups with Dynkin diagrams being a tree, the K(pi,1)-conjecture holds. We also establish the K(pi,1)-conjecture for another class of Artin groups whose Dynkin diagrams contain a cycle, which applies to some hyperbolic type Artin groups. This is based on a new approach to the K(pi,1)-conjecture for Artin groups.
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作者：Killip, Rowan; Laurens, Thierry; Visan, Monica
作者单位：University of California System; University of California Los Angeles; University of Wisconsin System; University of Wisconsin Madison
摘要：The Benjamin-Ono equation is shown to be well-posed, both on the line and on the circle, in the Sobolev spaces H(s )for s>-(1)|(2). The proof rests on a new gauge transfor-mation and benefits from our introduction of a modified Lax pair representation of the full hierarchy. As we will show, these developments yield important additional divi-dends beyond well-posedness, including (i) the unification of the diverse approaches to polynomial conservation laws; (ii) a generalization of G & eacute;r...
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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：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 $\end{document} and their chain-level Floer theory using ideas drawn from Hofer-Wysocki-Zehnder's theory of finite energy foliations. We associate to every collect...
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作者：Keevash, Peter; Lifshitz, Noam; Minzer, Dor
作者单位：University of Oxford; Hebrew University of Jerusalem; Massachusetts Institute of Technology (MIT)
摘要：A subset A of a group G is called product-free if there is no solution to a = bc with a, b, c all in A. It is easy to see that the largest product-free subset of the symmetric group Sn is obtained by taking the set of all odd permutations, i.e. S-n\A(n), where A(n) is the alternating group. In 1985 Babai and Sos (Eur. J. Comb. 6(2):101-114, 1985) conjectured that the group A(n) also contains a product-free set of constant density. This conjecture was refuted by Gowers (whose result was subsequ...
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作者：Zhuang, Ziquan
作者单位：Johns Hopkins University
摘要：We show that direct summands (or more generally, pure images) of klt type singularities are of klt type. As a consequence, we give a different proof of a recent result of Braun, Greb, Langlois and Moraga that reductive quotients of klt type singularities are of klt type.
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作者：Li, Dongchen; Turaev, Dmitry
作者单位：Imperial College London
摘要：A heterodimensional cycle is an invariant set of a dynamical system consisting of two hyperbolic periodic orbits with different dimensions of their unstable manifolds and a pair of orbits that connect them. For systems which are at least C 2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$C<^>{2}$\end{document} , we...
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作者：Oliver, Robert J. Lemke; Thorner, Jesse; Zaman, Asif
作者单位：Tufts University; University of Illinois System; University of Illinois Urbana-Champaign; University of Toronto
摘要：Let k be a number field and G be a finite group. Let F-k(G) (Q) be the family of number fields K with absolute discriminant D-K at most Q such that K/k is normal with Galois group isomorphic to G. If G is the symmetric group S-n or any transitive group of prime degree, then we unconditionally prove that for all K is an element of F-k(G) (Q) with at most O-epsilon(Q(epsilon)) exceptions, the L-functions associated to the faithful Artin representations of Gal(K/k) have a region of holomorphy and...
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作者：Linares, Pablo; Otto, Felix; Tempelmayr, Markus; Tsatsoulis, Pavlos
作者单位：Imperial College London; Max Planck Society; University of Munster; University of Bielefeld
摘要：In this paper, we explore the version of Hairer's regularity structures based on a greedier index set than trees, as introduced in (Otto et al. in A priori bounds for quasi-linear SPDEs in the full sub-critical regime, 2021, arXiv:2103.11039) and algebraically characterized in (Linares et al. in Comm. Am. Math. Soc. 3:1-64, 2023). More precisely, we construct and stochastically estimate the renormalized model postulated in (Otto et al. in A priori bounds for quasi-linear SPDEs in the full sub-...
