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• Universality of random matrices and local relaxation flow AI翻译
  作者：Erdos, Laszlo; Schlein, Benjamin; Yau, Horng-Tzer
  作者单位：University of Munich; University of Cambridge; Harvard University
  摘要：Consider the Dyson Brownian motion with parameter beta, where beta=1,2,4 corresponds to the eigenvalue flows for the eigenvalues of symmetric, hermitian and quaternion self-dual ensembles. For any beta a parts per thousand yen1, we prove that the relaxation time to local equilibrium for the Dyson Brownian motion is bounded above by N (-zeta) for some zeta > 0. The proof is based on an estimate of the entropy flow of the Dyson Brownian motion w.r.t. a pseudo equilibrium measure. As an applicati...
• Deformations of the hemisphere that increase scalar curvature AI翻译
  作者：Brendle, Simon; Marques, Fernando C.; Neves, Andre
  作者单位：Stanford University; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Imperial College London
  摘要：Consider a compact Riemannian manifold M of dimension n whose boundary a,M is totally geodesic and is isometric to the standard sphere S (n-1). A natural conjecture of Min-Oo asserts that if the scalar curvature of M is at least n(n-1), then M is isometric to the hemisphere S-+(n) equipped with its standard metric. This conjecture is inspired by the positive mass theorem in general relativity, and has been verified in many special cases. In this paper, we construct counterexamples to Min-Oo's ...
• Orbit inequivalent actions for groups containing a copy of F2 AI翻译
  作者：Ioana, Adrian
  作者单位：California Institute of Technology
  摘要：We prove that if a countable group Gamma contains a copy of F-2, then it admits uncountably many non orbit equivalent actions.
• C2 surface diffeomorphisms have symbolic extensions AI翻译
  作者：Burguet, David
  作者单位：Universite Paris Saclay
  摘要：We prove that C-2 surface diffeomorphisms have symbolic extensions, i.e. topological extensions which are subshifts over a finite alphabet. Following the strategy of Downarowicz and Maass (Invent. Math. 176: 617-636, 2009) we bound the local entropy of ergodic measures in terms of Lyapunov exponents. This is done by reparametrizing Bowen balls by contracting maps in a approach combining hyperbolic theory and Yomdin's theory.
• Even Galois representations and the Fontaine-Mazur conjecture AI翻译
  作者：Calegari, Frank
  作者单位：Northwestern University
  摘要：We prove, under mild hypotheses, that there are no irreducible two-dimensional ordinary even Galois representations of Gal((Q) over bar /Q) with distinct Hodge-Tate weights. This is in accordance with the Fontaine-Mazur conjecture. If K/Q is an imaginary quadratic field, we also prove ( again, under certain hypotheses) that Gal((Q) over bar /K) does not admit irreducible two-dimensional ordinary Galois representations of non-parallel weight.
• The Jacobian determinant revisited AI翻译
  作者：Brezis, Haim; Nguyen, Hoai-Minh
  作者单位：Rutgers University System; Rutgers University New Brunswick; Technion Israel Institute of Technology; New York University
• Intersection theory on Shimura surfaces II AI翻译
  作者：Howard, Benjamin
  作者单位：Boston College
  摘要：This is the third of a series of papers relating intersections of special cycles on the integral model of a Shimura surface to Fourier coefficients of Hilbert modular forms. More precisely, we embed the Shimura curve over ae associated to a rational quaternion algebra into the Shimura surface associated to the base change of the quaternion algebra to a real quadratic field. After extending the associated moduli problems over acurrency sign we obtain an arithmetic threefold with a embedded arit...
• Super duality and irreducible characters of ortho-symplectic Lie superalgebras AI翻译
  作者：Cheng, Shun-Jen; Lam, Ngau; Wang, Weiqiang
  作者单位：University of Virginia; Academia Sinica - Taiwan; National Cheng Kung University
  摘要：We formulate and establish a super duality which connects parabolic categories O for the ortho-symplectic Lie superalgebras and classical Lie algebras of BCD types. This provides a complete and conceptual solution of the irreducible character problem for the ortho-symplectic Lie superalgebras in a parabolic category O, which includes all finite dimensional irreducible modules, in terms of classical Kazhdan-Lusztig polynomials.
• The planetary N-body problem: symplectic foliation, reductions and invariant tori AI翻译
  作者：Chierchia, Luigi; Pinzari, Gabriella
  作者单位：Roma Tre University; University of Naples Federico II
  摘要：The 6n-dimensional phase space of the planetary (1 + n)-body problem (after the classical reduction of the total linear momentum) is shown to be foliated by symplectic leaves of dimension (6n - 2) invariant for the planetary Hamiltonian H. Such foliation is described by means of a new global set of Darboux coordinates related to a symplectic (partial) reduction of rotations. On each symplectic leaf H has the same form and it is shown to preserve classical symmetries. Further sets of Darboux co...
• A unified quantum SO(3) invariant for rational homology 3-spheres AI翻译
  作者：Beliakova, Anna; Buehler, Irmgard; Le, Thang
  作者单位：University of Zurich; University System of Georgia; Georgia Institute of Technology
  摘要：Given a rational homology 3-sphere M with |H (1)(M,acurrency sign)|=b and a link L inside M, colored by odd numbers, we construct a unified invariant I (M,L) belonging to a modification of the Habiro ring where b is inverted. Our unified invariant dominates the whole set of the SO(3) Witten-Reshetikhin-Turaev invariants of the pair (M,L). If b=1 and L=a..., I (M) coincides with Habiro's invariant of integral homology 3-spheres. For b > 1, the unified invariant defined by the third author is de...