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作者：McCammond, Jon; Sulway, Robert
作者单位：University of California System; University of California Santa Barbara
摘要：This article resolves several long-standing conjectures about Artin groups of Euclidean type. Specifically we prove that every irreducible Euclidean Artin group is a torsion-free centerless group with a decidable word problem and a finite-dimensional classifying space. We do this by showing that each of these groups is isomorphic to a subgroup of a group with an infinitet-ype Garside structure. The Garside groups involved are introduced here for the first time. They are constructed by applying...
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作者：Nemethi, Andras
作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Eotvos Lorand University; Basque Center for Applied Mathematics (BCAM)
摘要：We prove that the link of a complex normal surface singularity is an L-space if and only if the singularity is rational. This via a result of Hanselman et al. (Taut foliations on graph manifolds, 2015. arXiv: 1508.0591), proving the conjecture of Boyer et al. (Math Ann 356(4): 1213-1245, 2013), shows that a singularity link is not rational if and only if its fundamental group is left-orderable if and only if it admits a coorientable taut foliation.
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作者：Cao, Junyan; Pun, Mihai
作者单位：Universite Paris Cite; Sorbonne Universite; Korea Institute for Advanced Study (KIAS)
摘要：In this article we provide a proof of the Iitaka conjecture for algebraic fiber spaces over tori.
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作者：Valko, Benedek; Virag, Balint
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Toronto
摘要：We show that , the bulk limit of the Gaussian -ensembles is the spectrum of a self-adjoint random differential operator where is the positive definite matrix representation of hyperbolic Brownian motion with variance in logarithmic time. The result connects the Montgomery-Dyson conjecture about the process and the non-trivial zeros of the Riemann zeta function, the Hilbert-Plya conjecture and de Brange's attempt to prove the Riemann hypothesis. We identify the Brownian carousel as the Sturm-Li...
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作者：Das, Tushar; Simmons, David
作者单位：University of Wisconsin System; University of Wisconsin La Crosse; University of York - UK
摘要：We construct a self-affine sponge in R-3 whose dynamical dimension, i.e. the supremum of the Hausdorff dimensions of its invariant measures, is strictly less than its Hausdorff dimension. This resolves a long-standing open problem in the dimension theory of dynamical systems, namely whether every expanding repeller has an ergodic invariant measure of full Hausdorff dimension. More generally we compute the Hausdorff and dynamical dimensions of a large class of self-affine sponges, a problem tha...
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作者：Chhaibi, Reda; Najnudel, Joseph; Nikeghbali, Ashkan
摘要：We show in this paper that after proper scalings, the characteristic polynomial of a random unitary matrix converges to a random analytic function whose zeros, which are on the real line, form a determinantal point process with sine kernel. Our scaling is performed at the so-called microscopic level, that is we consider the characteristic polynomial at points whose distance to 1 has order 1 / n. We prove that the rescaled characteristic polynomial does not even have a moment of order one, henc...
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作者：Wang, Zhiren
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We show that the Mobius function is disjoint to every analytic skew product dynamical system on over a rotation of the circle.
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作者：Sam, Steven V.
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：Over a field of characteristic zero, we prove that for each r, there exists a constant C(r) so that the prime ideal of the rth secant variety of any Veronese embedding of any projective space is generated by polynomials of degree at most C(r). The main idea is to consider the coordinate ring of all of the ambient spaces of the Veronese embeddings at once by endowing it with the structure of a Hopf ring, and to show that its ideals are finitely generated. We also prove a similar statement for p...
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作者：Subag, Eliran
摘要：We analyze the statics for pure p-spin spherical spin glass models with p >= 3, at low enough temperature. With F-N,(beta) denoting the free energy, we compute the (logarithmic) second order term of NFN,(beta) and prove that, for an appropriate centering c(N),(beta), NFN,(beta) - c(N),beta is a tight sequence. We further establish the absence of temperature chaos. Those results follow from the following geometric picture we prove for the Gibbs measure, of interest by itself: asymptotically, th...
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作者：Breuil, Christophe; Hellmann, Eugen; Schraen, Benjamin
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; University of Munster; Institut Polytechnique de Paris; Ecole Polytechnique; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：Let p be a prime number and f an overconvergent p-adic automorphic form on a definite unitary group which is split at p. Assume that f is of classical weight and that its Galois representation is crystalline at p, then f is conjectured to be a classical automorphic form. We prove new cases of this conjecture in arbitrary dimensions by making crucial use of the patched eigenvariety constructed in Breuil et al. (Math. Ann. 2016).
