2期

最新文章

• 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...
• 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...
• 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...
• A proof of the instability of AdS for the Einstein-massless Vlasov system AI翻译
  作者：Moschidis, Georgios
  作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
  摘要：In recent years, the conjecture on the instability of Anti-de Sitter spacetime, put forward by Dafermos-Holzegel (Dynamic instability of solitons in 4 + 1 dimesnional gravity with negative cosmological constant, 2006. https://www.dpmms.cam.ac.uk/similar to md384/ADSinstability.pdf) and Dafermos (The Black Hole Stability problem, Talk at the Newton Institute, Cambridge, 2006. http://www-old.newton.ac.uk/webseminars/pg+ws/2006/gmx/1010/dafermos/) in 2006, has attracted a substantial amount of nu...
• Full derivation of the wave kinetic equation AI翻译
  作者：Deng, Yu; Hani, Zaher
  作者单位：University of Southern California; University of Michigan System; University of Michigan
  摘要：We provide the rigorous derivation of the wave kinetic equation from the cubic nonlinear Schrodinger (NLS) equation at the kinetic timescale, under a particular scaling law that describes the limiting process. This solves a main conjecture in the theory of wave turbulence, i.e. the kinetic theory of nonlinear wave systems. Our result is the wave analog of Lanford's theorem on the derivation of the Boltzmann kinetic equation from particle systems, where in both cases one takes the thermodynamic...
• The energy of dilute Bose gases II: the general case AI翻译
  作者：Fournais, Soren; Solovej, Jan Philip
  作者单位：Aarhus University; University of Copenhagen
  摘要：For a dilute system of non-relativistic bosons in 3 dimensions inter-acting through a positive, radially symmetric, potential v with scattering length a we prove that the ground state energy density satisfies the bound e(rho) >= 4 pi a rho(2)(1+128/15 root pi root rho a(3)+o(root rho a(3))), thereby proving a lower bound consistent with the Lee-Huang-Hang formula for the energy density. The proof allows for potentials with largeL1-norm, in particular, the case of hard core interactions is incl...
• Seshadri stratifications and standard monomial theory AI翻译
  作者：Chirivi, Rocco; Fang, Xin; Littelmann, Peter
  作者单位：University of Salento; RWTH Aachen University; University of Cologne
  摘要：We introduce the notion of a Seshadri stratification on an embedded projective variety. Such a structure enables us to construct a Newton-Okounkov simplicial complex and a flat degeneration of the projective variety into a union of toric varieties. We show that the Seshadri stratification provides a geometric setup for a standard monomial theory. In this framework, Lakshmibai-Seshadri paths for Schubert varieties get a geometric interpretation as successive vanishing orders of regular functions.
• K-stability and birational models of moduli of quartic K3 surfaces AI翻译
  作者：Ascher, Kenneth; DeVleming, Kristin; Liu, Yuchen
  作者单位：University of California System; University of California Irvine; University of Massachusetts System; University of Massachusetts Amherst; Northwestern University
  摘要：We show that the K-moduli spaces of log Fano pairs (P-3, cS) where S is a quartic surface interpolate between the GIT moduli space of quartic surfaces and the Baily-Borel compactification of moduli of quartic K3 surfaces as c varies in the interval (0, 1). We completely describe the wall crossings of these K-moduli spaces. As the main application, we verify Laza-O' Grady's prediction on the Hassett-Keel-Looijenga program for quartic K3 surfaces. We also obtain the K-moduli compactification of ...