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作者：Berger, Pierre
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite
摘要：We construct analytic symplectomorphisms of the cylinder or the sphere with zero or exactly two periodic points that are not conjugate to a rotation. In the case of the cylinder, we show that these symplectomorphisms can be chosen to be ergodic or, to the contrary, with local emergence of maximal order. In particular, this disproves a conjecture of Birkhoff (1941) and solves a problem of Herman (1998). One aspect of the proof provides a new approximation theorem; it enables the implementation ...
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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：Pan, Lue
作者单位：Princeton University; University of Michigan System; University of Michigan
摘要：This is a continuation of our previous work on the locally analytic vectors of the completed cohomology of modular curves. We construct differential operators on modular curves with infinite level at p in both holomorphic and anti-holomorphic directions. As applications, we reprove a classicality result of Emerton which says that every absolutely irreducible two dimensional Galois representation that is regular de Rham at p and appears in the completed cohomology of modular curves comes from a...
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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：Yang, Lei
作者单位：Institute for Advanced Study - USA; National University of Singapore
摘要：In this paper, we will prove an effective version of Ratner's equidistribution theorem for unipotent orbits in SL(3, R)/SL(3, Z) with a natural Diophantine condition.
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作者：Ruhstorfer, Lucas
作者单位：University of Wuppertal
摘要：In this paper we consider the inductive Alperin-McKay condition for quasi-isolated 2-blocks of exceptional groups of Lie type. Thereby, we complete the proof of the Alperin-McKay conjecture and Brauer's height zero conjecture for the prime 2.
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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：Dafermos, Mihalis; Luk, Jonathan
作者单位：Princeton University; University of Cambridge; Stanford University
摘要：We initiate a series of works where we study the interior of dynamical rotating vacuum black holes without symmetry. In the present paper, we take up the problem starting from appropriate Cauchy data for the Einstein vacuum equations defined on a hypersurface already within the black hole interior, representing the expected geometry just inside the event horizon. We prove that, for all such data, the maximal Cauchy evolution can be extended across a non-trivial piece of Cauchy horizon as a Lor...
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作者：Manolescu, Ciprian; Ozsvath, Peter s.; Thurston, Dylan p.
作者单位：Stanford University; Princeton University; Indiana University System; Indiana University Bloomington
摘要：We give combinatorial descriptions of the Heegaard Floer homology groups for arbitrary three-manifolds (with coefficients in Z/2Z). The descriptions are based on presenting the three-manifold as an integer surgery on a link in the three-sphere, and then using a grid diagram for the link. We also give combinatorial descriptions of the mod 2 Ozsv & aacute;th-Szab & oacute; mixed invariants of closed four-manifolds, also in terms of grid diagrams.
