3期

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...
• 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...
• 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...
• On the arithmetic Siegel-Weil formula for GSpin Shimura varieties AI翻译
  作者：Li, Chao; Zhang, Wei
  作者单位：Columbia University; Massachusetts Institute of Technology (MIT)
  摘要：We formulate and prove a local arithmetic Siegel-Weil formula for GSpin Rapoport-Zink spaces, which is a precise identity between the arithmetic intersection numbers of special cycles on GSpin Rapoport-Zink spaces and the derivatives of local representation densities of quadratic forms. As a first application, we prove a semi-global arithmetic Siegel-Weil formula as conjectured by Kudla, which relates the arithmetic intersection numbers of special cycles on GSpin Shimura varieties at a place o...
• Uniform Roe algebras of uniformly locally finite metric spaces are rigid AI翻译
  作者：Baudier, Florent P.; Braga, Bruno M.; Farah, Ilijas; Khukhro, Ana; Vignati, Alessandro; Willett, Rufus
  作者单位：Texas A&M University System; Texas A&M University College Station; York University - Canada; University of Cambridge; Universite Paris Cite; Sorbonne Universite; University of Hawaii System; University of Hawaii Manoa
  摘要：We show that if X and Y are uniformly locally finite metric spaces whose uniform Roe algebras, C-u* (X) and C-u* (Y), are isomorphic as C*-algebras, then X and Y are coarsely equivalent metric spaces. Moreover, we show that coarse equivalence between X and Y is equivalent to Morita equivalence between C-u* (X) and C-u* (Y). As an application, we obtain that if Gamma and Lambda are finitely generated groups, then the crossed products l(infinity)(Gamma) (sic)(r) Gamma and l(infinity)(Lambda) (si...
• Dualizing spheres for compact p-adic analytic groups and duality in chromatic homotopy AI翻译
  作者：Beaudry, Agnes; Goerss, Paul G.; Hopkins, Michael J.; Stojanoska, Vesna
  作者单位：University of Colorado System; University of Colorado Boulder; Northwestern University; Harvard University; University of Illinois System; University of Illinois Urbana-Champaign
  摘要：The primary goal of this paper is to study Spanier-Whitehead duality in the K (n)-local category. One of the key players in the K (n)-local category is the Lubin-Tate spectrum E-n, whose homotopy groups classify deformations of a formal group law of height n, in the implicit characteristic p. It is known that E-n is self-dual up to a shift; however, that does not fully take into account the action of the automorphism group G(n) of the formal group in question. In this paper we find that the G(...
• Charmenability of arithmetic groups of product type AI翻译
  作者：Bader, Uri; Boutonnet, Remi; Houdayer, Cyril; Peterson, Jesse
  作者单位：Weizmann Institute of Science; Universite de Bordeaux; Universite Paris Saclay; Vanderbilt University
  摘要：We discuss special properties of the spaces of characters and positive definite functions, as well as their associated dynamics, for arithmetic groups of product type. Axiomatizing these properties, we define the notions of charmenability and charfiniteness and study their applications to the topological dynamics, ergodic theory and unitary representation theory of the given groups. To do that, we study singularity properties of equivariant normal ucp maps between certain von Neumann algebras....