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作者：Eichinger, Benjamin; Lukic, Milivoje; Simanek, Brian
作者单位：Lancaster University; Technische Universitat Wien; Rice University; Baylor University
摘要：We describe an approach to universality limits for orthogonal polynomials on the real line which is completely local and uses only the boundary behavior of the Weyl m-function at the point. We show that bulk universality of the Christoffel-Darboux kernel holds for any point where the imaginary part of the m-function has a positive finite nontangential limit. This approach is based on studying a matrix version of the Christoffel- Darboux kernel and the realization that bulk universality for thi...
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作者：Eichinger, Benjamin; Lukic, Milivoje; Simanek, Brian
作者单位：Lancaster University; Technische Universitat Wien; Rice University; Baylor University
摘要：We describe an approach to universality limits for orthogonal polynomials on the real line which is completely local and uses only the boundary behavior of the Weyl m-function at the point. We show that bulk universality of the Christoffel-Darboux kernel holds for any point where the imaginary part of the m-function has a positive finite nontangential limit. This approach is based on studying a matrix version of the Christoffel- Darboux kernel and the realization that bulk universality for thi...
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作者：Karpeshina, Yulia; Parnovski, Leonid; Shterenberg, Roman
作者单位：University of Alabama System; University of Alabama Birmingham; University College London; University of London; University College London
摘要：We consider Schro & uml;dinger operators H = -triangle + V (x) in Rd, d >= 2, with quasi-periodic potentials V (x). We prove that the absolutely continuous spectrum of a generic H contains a semi-axis [lambda & lowast;, +infinity). We also construct a family of eigenfunctions of the absolutely continuous spectrum; these eigenfunctions are small perturbations of the exponentials. The proof is based on a version of the multi-scale analysis in the momentum space with several new ideas introduced ...
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作者：Castillo, Federico; Duarte, Daniel; Leyton-Alvarez, Maximiliano; Liendo, Alvaro
作者单位：Pontificia Universidad Catolica de Chile; Universidad Nacional Autonoma de Mexico; Universidad de Talca
摘要：In this paper we show that iterating Nash blowups or normalized Nash blowups does not resolve the singularities of algebraic varieties of dimension four or higher over an algebraically closed field of arbitrary characteristic.
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作者：Chen, Chi-Fang; Garza-Vargas, Jorge; Tropp, Joel A.; van Handel, Ramon
作者单位：University of California System; University of California Berkeley; Massachusetts Institute of Technology (MIT); Princeton University; California Institute of Technology
摘要：A family of random matrices XN = (X1N , ... , XdN ) is said to converge strongly to a family of bounded operators x = (x1, ... , xd) when parallel to P(XN,XN & lowast;)parallel to ->parallel to P(x,x & lowast;)parallel to for every noncommutative polynomial P. This phenomenon plays a key role in several recent breakthroughs on random graphs, geometry, and operator algebras. However, proofs of strong convergence are notoriously delicate and have relied largely on problem-specific methods. In th...
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作者：Dinur, Irit; Evra, Shai; Livne, Ron; Lubotzky, Alexander; Mozes, Shahar
作者单位：Weizmann Institute of Science; Institute for Advanced Study - USA; Hebrew University of Jerusalem; Weizmann Institute of Science
摘要：An explicit construction of locally testable codes of constant rate, constant distance and constant number of queries is given. Hence answering affirmatively the c3-problem.
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作者：Haim-Kislev, Pazit; Ostrover, Yaron
作者单位：Institute for Advanced Study - USA; Tel Aviv University
摘要：We present a counterexample to Viterbo's volume-capacity conjecture. This implies, in particular, that in contrast with a well-known conjecture, symplectic capacities do not coincide on the class of convex domains in the classical phase space.
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作者：Guth, Larry; Maynard, James
作者单位：Massachusetts Institute of Technology (MIT); University of Oxford; University of Oxford
摘要：We prove new bounds for how often Dirichlet polynomials can take large values. This gives improved estimates for a Dirichlet polynomial of length N taking values of size close to N3/4, which is the critical situation for several estimates in analytic number theory connected to prime numbers and the Riemann zeta function. As a consequence, we deduce a zero density estimate N(sigma, T) <= T30(1-sigma )/13+o(1) and asymptotics for primes in short intervals of length x17/30+o(1).
