-
作者：Bringmann, Bjoern; Deng, Yu; Nahmod, Andrea R.; Yue, Haitian
作者单位：Institute for Advanced Study - USA; Princeton University; University of Southern California; University of Massachusetts System; University of Massachusetts Amherst; ShanghaiTech University
摘要：We prove the invariance of the Gibbs measure under the dynamics of the three-dimensional cubic wave equation, which is also known as the hyperbolic Phi 34\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Phi <^>{4}_{3}$\end{document}-model. This result is the hyperbolic counterpart to seminal works on the parabolic P...
-
作者：Dougall, Rhiannon; Sharp, Richard
作者单位：Durham University; University of Warwick
摘要：This note corrects an error in our paper Anosov flows, growth rates on covers and group extensions of subshifts, Invent. Math. 223:445-483, 2021. This leaves our main results, Theorem 1.1, Corollary 1.2, Theorem 1.3 and Theorem 5.1, unchanged. We also fill a gap in the arguments presented in Sect. 9; this requires a small modification to the results in this section.
-
作者：Braun, Lukas; Greb, Daniel; Langlois, Kevin; Moraga, Joaquin
作者单位：University of Innsbruck; University of Duisburg Essen; Universidade Federal do Ceara; University of California System; University of California Los Angeles
摘要：We prove that the quotient of a klt type singularity by a reductive group is of klt type in characteristic 0. In particular, given a klt variety X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$X$\end{document} endowed with the action of a reductive group G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepacka...
-
作者：Barraquand, Guillaume; Corwin, Ivan; Yang, Zongrui
作者单位：Universite Paris Cite; Sorbonne Universite; Universite PSL; Ecole Normale Superieure (ENS); Columbia University
摘要：We prove that the stationary measures for the free-energy increment process for the geometric last passage percolation (LPP) and log-gamma polymer model on a diagonal strip is given by a marginal of a two-layer Gibbs measure with a simple and explicit description. This result is shown subject to certain restrictions on the parameters controlling the weights on the boundary of the strip. However, from this description and an analytic continuation argument we are able to access the stationary me...
-
作者：Martel, Yvan
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：For the Schr & ouml;dinger equation with a cubic-quintic, focusing-focusing nonlinearity in one space dimension, this article proves the local asymptotic completeness of the family of small standing solitary waves under even perturbations in the energy space. For this model, perturbative of the integrable cubic Schr & ouml;dinger equation for small solutions, the linearized equation around a small solitary wave has an internal mode, whose contribution to the dynamics is handled by the Fermi go...
-
作者：Stadler, Stephan
作者单位：Max Planck Society
摘要：This belongs to a series of papers motivated by Ballmann's Higher Rank Rigidity Conjecture. We prove the following. Let X be a CAT(0) space with a geometric group action Gamma curved right arrow X. Suppose that every geodesic in X lies in an n-flat, n >= 2. If X contains a periodic n-flat which does not bound a flat (n + 1)-half-space, then X is a Riemannian symmetric space, a Euclidean building or non-trivially splits as a metric product. This generalizes the Higher Rank Rigidity Theorem for ...
-
作者：Chodosh, Otis; Daniels-Holgate, J. M.; Schulze, Felix
作者单位：Stanford University; Hebrew University of Jerusalem; University of Warwick
摘要：We prove Ilmanen's resolution of point singularities conjecture by establishing short-time smoothness of the level set flow of a smooth hypersurface with isolated conical singularities. This shows how the mean curvature flow evolves through asymptotically conical singularities. Precisely, we prove that the level set flow of a smooth hypersurface Mn subset of Rn+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy...
-
作者：Krah, Johannes
作者单位：University of Bielefeld
摘要：We construct a non-full exceptional collection of maximal length consisting of line bundles on the blow-up of the projective plane in 10 general points. As a consequence, the orthogonal complement of this collection is a universal phantom category. This provides a counterexample to a conjecture of Kuznetsov and to a conjecture of Orlov.
-
作者：Chow, Sam; Yang, Lei
作者单位：University of Warwick; Institute for Advanced Study - USA
摘要：Given any line in the plane, we strengthen the Littlewood conjecture by two logarithms for almost every point on the line, thereby generalising the fibre result of Beresnevich, Haynes, and Velani. To achieve this, we prove an effective asymptotic equidistribution result for one-parameter unipotent orbits in SL(3, R)/SL(3, Z). We also provide a complementary convergence statement, by developing the structural theory of dual Bohr sets: at the cost of a slightly stronger Diophantine assumption, t...
-
作者：Iyengar, Srikanth B.; Khare, Chandrashekhar B.; Manning, Jeffrey
作者单位：Utah System of Higher Education; University of Utah; University of California System; University of California Los Angeles
摘要：We define a congruence module Psi(A)(M) associated to a surjective O\-algebra morphism lambda:A -> O, with O a discrete valuation ring, A a complete noetherian local O-algebra regular at p, the kernel of lambda, and M a finitely generated A-module. We establish a numerical criterion for M to have a free direct summand over A of positive rank. It is in terms of the lengths of Psi(A)(M) and the torsion part of p/p(2). It generalizes results of Wiles, Lenstra, and Diamond, that deal with the case...
