Inventiones mathematicae

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• 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...
• Potential automorphy for G Ln AI翻译
  作者：Qian, Lie
  作者单位：Stanford University
  摘要：We prove potential automorphy results for a single Galois representation G(F) -> GL(n)((Q) over bar (l)) where F is a CM number field. The strategy is to use the p, q switch trick to go between the p-adic and q-adic realisation of a certain variant of the Dwork motive. We choose this variant to break self-duality shape of the motives, but not the Hodge-Tate weights. Another key result to prove is that certain p-adic representations we choose that come from the Dwork motives is ordinarily autom...
• 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...
• Moment maps and cohomology of non-reductive quotients AI翻译
  作者：Berczi, Gergely; Kirwan, Frances
  作者单位：Aarhus University; University of Oxford
  摘要：Let H be a complex linear algebraic group with internally graded unipotent radical acting on a complex projective variety X. Given an ample linearisation of the action and an associated Fubini-Study Kahler form which is invariant for a maximal compact subgroup Q of H, we define a notion of moment map for the action of H, and under suitable conditions (that the linearisation is well -adapted and semistability coincides with stability) we describe the (non -reductive) GIT quotient X//H introduce...
• 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...