Inventiones mathematicae

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• Modularity lifting beyond the Taylor-Wiles method AI翻译
  作者：Calegari, Frank; Geraghty, David
  作者单位：University of Chicago; Boston College
  摘要：We prove new modularity lifting theorems for p-adic Galois representations in situations where the methods of Wiles and Taylor-Wiles do not apply. Previous generalizations of these methods have been restricted to situations where the automorphic forms in question contribute to a single degree of cohomology. In practice, this imposes several restrictions-one must be in a Shimura variety setting and the automorphic forms must be of regular weight at infinity. In this paper, we essentially show h...
• The holomorphic couch theorem AI翻译
  作者：Bourque, Maxime Fortier
  作者单位：University of Toronto
  摘要：We prove that if two conformal embeddings between Riemann surfaces with finite topology are homotopic, then they are isotopic through conformal embeddings. Furthermore, we show that the space of all conformal embeddings in a given homotopy class is homotopy equivalent to a point, a circle, a torus, or the unit tangent bundle of the codomain, depending on the induced homomorphism on fundamental groups. Quadratic differentials play a central role in the proof.
• Modular irreducibility of cuspidal unipotent characters AI翻译
  作者：Dudas, Olivier; Malle, Gunter
  作者单位：Universite Paris Cite; University of Kaiserslautern
  摘要：We prove a long-standing conjecture of Geck which predicts that cuspidal unipotent characters remain irreducible after -reduction. To this end, we construct a progenerator for the category of representations of a finite reductive group coming from generalised Gelfand-Graev representations. This is achieved by showing that cuspidal representations appear in the head of generalised Gelfand-Graev representations attached to cuspidal unipotent classes, as defined and studied in Geck and Malle (J L...
• Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras AI翻译
  作者：Kang, Seok-Jin; Kashiwara, Masaki; Kim, Myungho
  作者单位：Kyoto University; Seoul National University (SNU); Seoul National University (SNU); Kyung Hee University
  摘要：Let J be a set of pairs consisting of good -modules and invertible elements in the base field . The distribution of poles of normalized R-matrices yields Khovanov-Lauda-Rouquier algebras for each . We define a functor from the category of graded -modules to the category of -modules. The functor sends convolution products of finite-dimensional graded -modules to tensor products of finite-dimensional -modules. It is exact if is of finite type A, D, E. If is the fundamental representation of of w...
• The simplification of singularities of Lagrangian and Legendrian fronts AI翻译
  作者：Alvarez-Gavela, Daniel
  作者单位：Stanford University
  摘要：We establish a full h-principle (close, relative, parametric) for the simplification of singularities of Lagrangian and Legendrian fronts. More precisely, we prove that if there is no homotopy theoretic obstruction to simplifying the singularities of tangency of a Lagrangian or Legendrian submanifold with respect to an ambient foliation by Lagrangian or Legendrian leaves, then the simplification can be achieved by means of a Hamiltonian isotopy.
• Time quasi-periodic gravity water waves in finite depth AI翻译
  作者：Baldi, Pietro; Berti, Massimiliano; Haus, Emanuele; Montalto, Riccardo
  作者单位：University of Naples Federico II; International School for Advanced Studies (SISSA); University of Zurich
  摘要：We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutionsnamely periodic and even in the space variable xof a bi-dimensional ocean with finite depth under the action of pure gravity. Such a result holds for all the values of the depth parameter in a Borel set of asymptotically full measure. This is a small divisor problem. The main difficulties are the fully nonlinear nature of the gravity water waves equationsthe hi...
• Attracting currents and equilibrium measures for quasi-attractors of AI翻译
  作者：Taflin, Johan
  作者单位：Universite Bourgogne Europe
  摘要：Let f be a holomorphic endomorphism of of degree d. For each quasi-attractor of f we construct a finite set of currents with attractive behaviors. To every such attracting current is associated an equilibrium measure which allows for a systematic ergodic theoretical approach in the study of quasi-attractors of . As a consequence, we deduce that there exist at most countably many quasi-attractors, each one with topological entropy equal to a multiple of . We also show that the study of these an...
• Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures AI翻译
  作者：Liero, Matthias; Mielke, Alexander; Savare, Giuseppe
  作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Pavia
  摘要：We develop a full theory for the new class of Optimal Entropy-Transport problems between nonnegative and finite Radon measures in general topological spaces. These problems arise quite naturally by relaxing the marginal constraints typical of Optimal Transport problems: given a pair of finite measures (with possibly different total mass), one looks for minimizers of the sum of a linear transport functional and two convex entropy functionals, which quantify in some way the deviation of the marg...
• Expanding large global solutions of the equations of compressible fluid mechanics AI翻译
  作者：Hadzic, Mahir; Jang, Juhi
  作者单位：University of Southern California; Korea Institute for Advanced Study (KIAS)
  摘要：Without any symmetry assumptions on the initial data we construct global-in-time unique solutions to the vacuum free boundary three-dimensional isentropic compressible Euler equations when the adiabatic exponent. lies in the interval (1, 53]. Our initial data lie sufficiently close to the expanding compactly supported affine motions recently constructed by Sideris and they satisfy the physical vacuum boundary condition.
• Point vortex dynamics as zero-radius limit of the motion of a rigid body in an irrotational fluid AI翻译
  作者：Glass, Olivier; Munnier, Alexandre; Sueur, Franck
  作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Universite de Lorraine; Inria; Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Inria
  摘要：The point vortex system is usually considered as an idealized model where the vorticity of an ideal incompressible two-dimensional fluid is concentrated in a finite number of moving points. In the case of a single vortex in an otherwise irrotational ideal fluid occupying a bounded and simply-connected two-dimensional domain the motion is given by the so-called Kirchhoff-Routh velocity which depends only on the domain. The main result of this paper establishes that this dynamics can also be obt...