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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...
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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...
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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...
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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...
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作者：Fei, Mingwen; Lin, Fanghua; Wang, Wei; Zhang, Zhifei
作者单位：Anhui Normal University; New York University; Zhejiang University; Peking University
摘要：In this paper, we consider the sharp interface limit of a matrix-valued Allen-Cahn equation, which takes the form: partial derivative(t)A = Delta A - epsilon(-2) (AA(T)A - A) with A: Omega subset of R-m -> R-nxn. We show that the sharp interface system is a two-phases flow system: the interface evolves according to the motion by mean curvature; in the two bulk phase regions, the solution obeys the heat flow of harmonic maps with values in O+(n) and O-(n) (represent the sets of n u n orthogonal...
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作者：Xu, Xingwang; Ye, Jian
作者单位：Nanjing University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：This article is devoted to the study of the closed vacuum static spaces. Based on the argument of maximum principle, we show that three-dimensional closed vacuum static spaces with scalar curvature 6 must be isometric to either the standard unit sphere S-3 (1) or a finite quotient of the torus S-1 (root 1/3) x S-2 (root 1/3).
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作者：Caro, Jerson; Pasten, Hector
作者单位：Pontificia Universidad Catolica de Chile
摘要：Building on work by Chabauty from 1941, Coleman proved in 1985 an explicit bound for the number of rational points of a curve C of genus g = 2 defined over a number field F, with Jacobian of rank at most g - 1. Namely, in the case F = Q, if p > 2g is a prime of good reduction, then the number of rational points of C is at most the number of F-p-points plus a contribution coming from the canonical class of C. We prove a result analogous to Coleman's bound in the case of a hyperbolic surface X o...
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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...
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作者：Le, Daniel; Le Hung, Bao V.; Levin, Brandon; Morra, Stefano
作者单位：Purdue University System; Purdue University; Northwestern University; Rice University; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-VIII
摘要：We construct projective varieties in mixed characteristic whose singularities model, in generic cases, those of tamely potentially crystalline Galois deformation rings for unramified extensions of Q(p) with small regular Hodge-Tate weights. We establish several significant facts about their geometry including a unibranch property at special points and a representation theoretic description of the irreducible components of their special fibers. We derive from these geometric results a number of...
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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.
