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作者：Eilat, Matan; Klartag, Bo'az
作者单位：Weizmann Institute of Science
摘要：Let M be a complete, connected Riemannian surface and suppose that S subset of M is a discrete subset. What can we learn about M from the knowledge of all Riemannian distances between pairs of points of S? We prove that if the distances in S correspond to the distances in a 2-dimensional lattice, or more generally in an arbitrary net in R-2, then M is isometric to the Euclidean plane. We thus find that Riemannian embeddings of certain discrete metric spaces are rather rigid. A corollary is tha...
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作者：Klingler, B.; Otwinowska, A.
作者单位：Humboldt University of Berlin
摘要：Given V a polarizable variation of Z-Hodge structures on a smooth connected complex quasi-projective variety S, the Hodge locus for V-circle times is the set of closed points s of S where the fiber V-s has more Hodge tensors than the very general one. A classical result of Cattani, Deligne and Kaplan states that the Hodge locus for V-circle times is a countable union of closed irreducible algebraic subvarieties of S, called the special subvarieties of S for V. Under the assumption that the adj...
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作者：Buckmaster, T.; Germain, P.; Hani, Z.; Shatah, J.
作者单位：Princeton University; University of Michigan System; University of Michigan
摘要：Consider the cubic nonlinear Schrodinger equation set on a d-dimensional torus, with data whose Fourier coefficients have phases which are uniformly distributed and independent. We show that, on average, the evolution of the moduli of the Fourier coefficients is governed by the so-called wave kinetic equation, predicted in wave turbulence theory, on a nontrivial timescale.
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作者：Hubner, Katharina; Schmidt, Alexander
作者单位：Hebrew University of Jerusalem; Ruprecht Karls University Heidelberg
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作者：Chen, Gao
作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS
摘要：In this paper, we prove that for any Kahler metrics omega(0) and chi on M, there exists a Kahler metric omega(phi) = omega(0) + root-1 partial derivative(partial derivative) over bar phi > 0 satisfying the J-equation tr omega(phi)chi = c if and only if (M, [omega(0)], [chi]) is uniformly J-stable. As a corollary, we find a sufficient condition for the existence of constant scalar curvature Kahler metrics with c(1) < 0. Using the same method, we also prove a similar result for the supercritical...
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作者：Chan, Kei Yuen
作者单位：Fudan University
摘要：Let F be a non-Archimedean local field. This paper studies homological properties of irreducible smooth representations restricted from GL(n+1)( F) to GL(n)( F). A main result shows that each Bernstein component of an irreducible smooth representation of GL(n+1)( F) restricted to GL(n)(F) is indecomposable. We also classify all irreducible representations which are projective when restricting from GL(n+1)( F) to GL(n)( F). A main tool of our study is a notion of left and right derivatives, ext...
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作者：Chen, Xuemiao; Sun, Song
作者单位：University System of Maryland; University of Maryland College Park; University of California System; University of California Berkeley
摘要：In this paper we give a complete algebro-geometric characterization of analytic tangent cones of admissible Hermitian-Yang-Mills connections over any reflexive sheaves.
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作者：Ding, Jian; Xia, Jiaming
作者单位：University of Pennsylvania
摘要：We study the random field Ising model on Z(2) where the external field is given by i.i.d. Gaussian variables with mean zero and positive variance. We show that the effect of boundary conditions on the magnetization in a finite box decays exponentially in the distance to the boundary.
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作者：Castillejos, Jorge; Evington, Samuel; Tikuisis, Aaron; White, Stuart; Winter, Wilhelm
作者单位：KU Leuven; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; University of Oxford; University of Ottawa; University of Glasgow; University of Munster
摘要：We compute the nuclear dimension of separable, simple, unital, nuclear, Z-stable C*-algebras. This makes classification accessible from Z-stability and in particular brings large classes of C*-algebras associated to free and minimal actions of amenable groups on finite dimensional spaces within the scope of the Elliott classification programme.
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作者：Lecouturier, Emmanuel
作者单位：Tsinghua University
摘要：Let N and p be primes such that p divides the numerator of N-1/12. In this paper, we study the rank g(p) of the completion of the Hecke algebra acting on cuspidal modular forms of weight 2 and level Gamma(0)(N) at the p-maximal Eisenstein ideal. We give in particular an explicit criterion to know if g(p) >= 3, thus answering partially a question of Mazur. In order to study g(p), we develop the theory of higher Eisenstein elements, and compute the first few such elements in four different Hecke...
