2023

最新文章

• Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups AI翻译
  作者：Monod, Nicolas; Nariman, Sam
  作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Purdue University System; Purdue University
  摘要：We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring generated by the bounded Euler class. These seem to be the first examples of groups for which the entire bounded cohomology can be described without being trivial. We further prove that the C-r-diffeomorphisms groups of the circle and of the c...
• Unbounded Hankel operators and the flow of the cubic Szego equation AI翻译
  作者：Gerard, Patrick; Pushnitski, Alexander
  作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of London; King's College London
  摘要：We prove that, for any Hankel operator with a symbol from the Hardy class H-2, the maximal and minimal domains coincide. As an application, we prove that the evolution flow of the cubic Szeg & oacute; equation on the unit circle can be continuously extended to the whole class H-2.
• Random walks, spectral gaps, and Khintchine's theorem on fractals AI翻译
  作者：Khalil, Osama; Luethi, Manuel
  作者单位：Utah System of Higher Education; University of Utah; Tel Aviv University
  摘要：This work addresses problems on simultaneous Diophantine approximation on fractals, motivated by a long standing problem of Mahler regarding Cantor's middle 1/3 set. We obtain the first instances where a complete analogue of Khintchine's Theorem holds for fractal measures. Our results apply to fractals which are self-similar by a system of rational similarities of R-d (for any d >= 1) and have sufficiently small Hausdorff co-dimension. A concrete example of such measures in the context of Mahl...
• On the conformal walk dimension: quasisymmetric uniformization for symmetric diffusions AI翻译
  作者：Kajino, Naotaka; Murugan, Mathav
  作者单位：Kobe University; Kyoto University; University of British Columbia
  摘要：We introduce the notion of conformal walk dimension, which serves as a bridge between elliptic and parabolic Harnack inequalities. The importance of this notion is due to the fact that, for a given strongly local, regular symmetric Dirichlet space in which every metric ball has compact closure (MMD space), the finiteness of the conformal walk dimension characterizes the conjunction of the metric doubling property and the elliptic Harnack inequality. Roughly speaking, the conformal walk dimensi...
• Zeta morphisms for rank two universal deformations AI翻译
  作者：Nakamura, Kentaro
  作者单位：Saga University
  摘要：In this article, we construct zeta morphisms for the universal deformations of odd absolutely irreducible two dimensional mod p Galois representations satisfying some mild assumptions, and prove that our zeta morphisms interpolate Kato's zeta morphisms for Galois representations associated to Hecke eigen cusp newforms. The existence of such morphisms was predicted by Kato's generalized Iwasawa main conjecture. Based on Kato's original construction, we construct our zeta morphisms using many de...
• Tautological classes of matroids AI翻译
  作者：Berget, Andrew; Eur, Christopher; Spink, Hunter; Tseng, Dennis
  作者单位：Western Washington University; Stanford University; Harvard University
  摘要：We introduce certain torus-equivariant classes on permutohedral varieties which we call tautological classes of matroids as a new geometric framework for studying matroids. Using this framework, we unify and extend many recent developments in matroid theory arising from its interaction with algebraic geometry. We achieve this by establishing a Chow-theoretic description and a log-concavity property for a 4 -variable transformation of the Tutte polynomial, and by establishing an exceptional Hir...
• Banach property (T) for SLn(Z) and its applications AI翻译
  作者：Oppenheim, Izhar
  作者单位：Ben-Gurion University of the Negev
  摘要：We prove that a large family of higher rank simple Lie groups (including SLn(R) for n >= 3) and their lattices have Banach property (T) with respect to all super-reflexive Banach spaces. Two consequences of this result are: First, we deduce Banach fixed point properties with respect to all super-reflexive Banach spaces for a large family of higher rank simple Lie groups. For example, we show that for every n >= 4, the group SLn(R) and all its lattices have the Banach fixed point property with ...
• The maximal subgroups of the exceptional groups F4(q), E6(q) and 2E6(q) and related almost simple groups AI翻译
  作者：Craven, David A. A.
  作者单位：University of Birmingham
  摘要：This article produces a complete list of all maximal subgroups of the finite simple groups of type F-4, E-6 and twisted E-6 over all finite fields. Along the way, we determine the collection of Lie primitive almost simple subgroups of the corresponding algebraic groups. We give the stabilizers under the actions of outer automorphisms, from which one can obtain complete information about the maximal subgroups of all almost simple groups with socle one of these groups. We also provide a new maxi...
• Polya's conjecture for Euclidean balls AI翻译
  作者：Filonov, Nikolay; Levitin, Michael; Polterovich, Iosif; Sher, David A.
  作者单位：Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Scientific Centre of the Russian Academy of Sciences; Saint Petersburg State University; University of Reading; Universite de Montreal; DePaul University
  摘要：The celebrated Polya's conjecture (1954) in spectral geometry states that the eigenvalue counting functions of the Dirichlet and Neumann Laplacian on a bounded Euclidean domain can be estimated from above and below, respectively, by the leading term of Weyl's asymptotics. Polya's conjecture is known to be true for domains which tile Euclidean space, and, in addition, for some special domains in higher dimensions. In this paper, we prove Polya's conjecture for the disk, making it the first non-...
• Distributed algorithms, the Lovasz Local Lemma, and descriptive combinatorics AI翻译
  作者：Bernshteyn, Anton
  作者单位：University System of Georgia; Georgia Institute of Technology
  摘要：In this paper we consider coloring problems on graphs and other combinatorial structures on standard Borel spaces. Our goal is to obtain sufficient conditions under which such colorings can be made well-behaved in the sense of topology or measure. To this end, we show that such well-behaved colorings can be produced using certain powerful techniques from finite combinatorics and computer science. First, we prove that efficient distributed coloring algorithms (on finite graphs) yield well-behav...