2022

最新文章

• Concentration on the Boolean hypercube via pathwise stochastic analysis AI翻译
  作者：Eldan, Ronen; Gross, Renan
  作者单位：Weizmann Institute of Science
  摘要：We develop a new technique for proving concentration inequalities which relate the variance and influences of Boolean functions. Using this technique, we 1. Settle a conjecture of Talagrand (Combinatorica 17(2):275-285, 1997), proving that integral({-1,1}n) root h(f) (x)d mu(x) >= C . Var (f) . (log (1/Sigma Inf(i)(2)(f)))(1/2), where h(f) (x) is the number of edges at x along which f changes its value, mu(x) is the uniform measure on {-1, 1}(n), and Inf(i) (f) is the influence of the i-th coo...
• Sharp nonuniqueness for the Navier-Stokes equations AI翻译
  作者：Cheskidov, Alexey; Luo, Xiaoyutao
  作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Institute for Advanced Study - USA; Duke University
  摘要：In this paper, we prove a sharp nonuniqueness result for the incompressible Navier-Stokes equations in the periodic setting. In any dimension d >= 2 and given any p < 2, we show the nonuniqueness of weak solutions in the class (LtL infinity)-L-p, which is sharp in view of the classical Ladyzhenskaya-Prodi-Serrin criteria. The proof is based on the construction of a class of non-Leray-Hopf weak solutions. More specifically, for any p < 2, q < infinity, and epsilon > 0, we construct non-Leray-Ho...
• Babai's conjecture for high-rank classical groups with random generators AI翻译
  作者：Eberhard, Sean; Jezernik, Urban
  作者单位：University of Cambridge; University of Ljubljana
  摘要：Let G = SCln(q) be a quasisimple classical group with n large, and let x(1),..., x(k) is an element of G be random, where k >= q(C). We show that the diameter of the resulting Cayley graph is bounded by q(2)n(O(1)) with probability 1 - o(1). In the particular case G = SLn(p) with p a prime of bounded size, we show that the same holds for k = 3.
• Degenerating Kahler-Einstein cones, locally symmetric cusps, and the Tian-Yau metric AI翻译
  作者：Biquard, Olivier; Guenancia, Henri
  作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS)
  摘要：Let X be a complex projectivemanifold and let D subset of X be a smooth divisor. In this article, we are interested in studying limits when ss -> 0 of Kahler-Einstein metrics omega(ss) with a cone singularity of angle 2 pi ss along D. In our first result, we assume that X \ D is a locally symmetric space and we show that omega(ss) converges to the locally symmetric metric and further give asymptotics of omega(ss) when X \ D is a ball quotient. Our second result deals with the case when X is Fa...
• Billiards, heights, and the arithmetic of non-arithmetic groups AI翻译
  作者：McMullen, Curtis T.
  作者单位：Harvard University
  摘要：In this paper we introduce a new height on P-1 (K) associated to an Abelian variety with real multiplication by K, and use it to study non-arithmetic triangle groups, Teichintiller curves, and billiards in lattice polygons. Complementary results on matrix coefficients and measures are obtained using modular symbols. In particular, we show the matrix entries m of the classical Hecke group Delta(2, 5, infinity) are constrained by the condition that -gamma(-2)(m'/m) lies in a countable, closed se...
• Squarefree values of polynomial discriminants I AI翻译
  作者：Bhargava, Manjul; Shankar, Arul; Wang, Xiaoheng
  作者单位：Princeton University; University of Toronto; University of Waterloo
  摘要：We determine the density of monic integer polynomials of given degree n > 1 that have squarefree discriminant; in particular, we prove for the first time that the lower density of such polynomials is positive. Similarly, we prove that the density of monic integer polynomials f (x), such that f (x) is irreducible and Z[x]/(f (x)) is the ring of integers in its fraction field, is positive, and is in fact given by zeta (2)(-1). It also follows from our methods that there are >> X1/2+1/n monogenic...
• Continuity properties of Lyapunov exponents for surface diffeomorphisms AI翻译
  作者：Buzzi, Jerome; Crovisier, Sylvain; Sarig, Omri
  作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Weizmann Institute of Science
  摘要：We study the entropy and Lyapunov exponents of invariant measures mu for smooth surface diffeomorphisms f, as functions of (f, mu). The main result is an inequality relating the discontinuities of these functions. One consequence is that for a C-infinity surface diffeomorphism, on any set of ergodic measures with entropy bounded away from zero, continuity of the entropy implies continuity of the exponents. Another consequence is the upper semicontinuity of the Hausdorff dimension on the set of...
• On contact type hypersurfaces in 4-space AI翻译
  作者：Mark, Thomas E.; Tosun, Bulent
  作者单位：University of Virginia; University of Alabama System; University of Alabama Tuscaloosa
  摘要：We consider constraints on the topology of closed 3-manifolds that can arise as hypersurfaces of contact type in standard symplectic R-4. Using an obstruction derived from Heegaard Hoer homology we prove that no Brieskorn homology sphere admits a contact type embedding in R-4 , a result that has bearing on conjectures of Gompf and Kollar. This implies in particular that no rationally convex domain in C-2 has boundary diffeomorphic to a Brieskorn sphere. We also give infinitely many examples of...
• Local P entropy and stabilized automorphism groups of subshifts AI翻译
  作者：Schmieding, Scott
  作者单位：University of Denver
  摘要：For a homeomorphism T : X -> X of a compact metric space X, the stabilized automorphism group Aut((infinity))( T) consists of all self-homeomorphisms of X which commute with some power of T. Motivated by the study of these groups in the context of shifts of finite type, we introduce a certain entropy for groups called local P entropy. We show that when (X, T) is a non-trivial mixing shift of finite type, the local P entropy of the group Aut((infinity))(T) is determined by the topological entro...
• Quasimap wall-crossing for GIT quotients AI翻译
  作者：Zhou, Yang
  作者单位：Fudan University
  摘要：In this paper, we prove a wall-crossing formula for epsilon-stable quasimaps to GIT quotients conjectured by Ciocan-Fontanine and Kim, for all targets in all genera, including the orbifold case. We prove that stability conditions in adjacent chambers give equivalent invariants, provided that both chambers are stable. In the case of genus-zero quasimaps with one marked point, we compute the invariants in the left-most stable chamber in terms of the small I-function. Using this we prove that the...