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作者：Chaika, Jon; Forni, Giovanni
作者单位：Utah System of Higher Education; University of Utah; University System of Maryland; University of Maryland College Park
摘要：We prove that there exists a G delta dense set of (non-rational) polygons such the billiard flow is weakly mixing with respect to the Liouville measure (on the unit tangent bundle to the billiard). This follows, via a Baire category argument, from showing that for any translation surface the product of the flows in almost every pair of directions is ergodic with respect to Lebesgue measure. This in turn is proven by showing that for every translation surface the flows in almost every pair of d...
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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：De Saxce, Nicolas
作者单位：Centre National de la Recherche Scientifique (CNRS)
摘要：We study intrinsic diophantine approximation on Grassmann varieties. Using a new correspondence between the diophantine properties of a linear subspace x in Rd and certain diagonal orbits in the space of lattices, we are able to solve some problems suggested by Schmidt in 1967. In particular, we obtain a version of Dirichlet's principle in this setting with an optimal exponent.
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作者：Cabanes, MARc; Spaeth, Britta
作者单位：Sorbonne Universite; Universite Paris Cite; University of Wuppertal
摘要：We prove that for any prime P, any finite group has as many irreducible complex characters of degree prime to P as the normalizers of its Sylow P-subgroups. This equality was conjectured by John McKay in 1971. The conjecture was reduced by Isaacs-Malle-Navarro (2007) to a conjecture on representations, linear and projective, of finite simple groups that we finish proving here using the classification of those groups. We study mainly characters of normalizers N-G(S)(F )of Sylow d-tori S (d >= 3...
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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：Burungale, Ashay A.; Tian, Ye
作者单位：California Institute of Technology; University of Texas System; University of Texas Austin; Chinese Academy of Sciences; Nanjing Institute of Geology & Paleontology, CAS; Chinese Academy of Sciences; Nanjing Institute of Geology & Paleontology, CAS; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS
摘要：Let E be a CM elliptic curve defined over Q and p a prime. We show that corankZp Selp infinity (E/Q) = 0 =double right arrow ords=1L(s, E/Q) = 0 for the p infinity- Selmer group Selp infinity(E/Q) and the complex L-function L(s, E/Q). Along with Smith's work on the distribution of 2 infinity-Selmer groups, this leads to the first instance of the even parity Goldfeld conjecture: For 50% of the positive square-free integers n, we have ords=1L(s, E/Q(n)) = 0, where E(n) : ny2 = x3-x is a quadrati...
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作者：Giri, Vikram; Kwon, Hyunju; Novack, Matthew
作者单位：University of Zurich; Swiss Federal Institutes of Technology Domain; ETH Zurich; Purdue University System; Purdue University
摘要：In this work, we prove the L-3-based strong Onsager conjecture for the three-dimensional Euler equations. Our main theorem states that there exist weak solutions which dissipate the total kinetic energy, satisfy the local energy inequality, and belong to C-t(0)(W-1/3-,W-3 boolean AND L infinity-). More precisely, for every beta < 1/3, we can construct such solutions in the space C-t(0)(B-3,infinity(beta) boolean AND 1/L1-3 beta).
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作者：Nelson, Paul d.
作者单位：Aarhus University
摘要：We determine the asymptotic quantum variance of microlo cal lifts of Hecke-Maass cusp forms on the arithmetic compact hyperbolic surfaces attached to maximal orders in quaternion algebras. Our result extends those for the non-compact modular surface obtained by Luo-Sarnak-Zhao, whose method required a cusp. The global arguments in our proof involve an analytic study of the theta correspondence, the interplay between additive and multiplicative harmonic analysis on quaternion algebras, the equi...
