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作者：Idrissi, Najib
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove the validity over R of a commutative differential graded algebra model of configuration spaces for simply connected closed smooth manifolds, answering a conjecture of Lambrechts-Stanley. We get as a result that the real homotopy type of such configuration spaces only depends on the real homotopy type of the manifold. We moreover prove, if the dimension of the manifold is at least 4, that our model is compatible with the action of the Fulton-MacPherson operad (weakly equivalent to the ...
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作者：Goldstein, Michael; Schlag, Wilhelm; Voda, Mircea
作者单位：University of Toronto; Yale University; University of Chicago
摘要：We study multi-frequency quasiperiodic Schrodinger operators on Z. We prove that for a large real analytic potential satisfying certain restrictions the spectrum consists of a single interval. The result is a consequence of a criterion for the spectrum to contain an interval at a given location that we establish non-perturbatively in the regime of positive Lyapunov exponent.
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作者：Antieau, Benjamin; Auel, Asher; Ingalls, Colin; Krashen, Daniel; Lieblich, Max
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Yale University; Rutgers University System; Rutgers University New Brunswick; Rutgers University Newark; University of Washington; University of Washington Seattle
摘要：The standard period-index conjecture for Brauer groups of p-adic surfaces S predicts that ind(alpha) vertical bar per(alpha)3 for every alpha is an element of Br(Q(p)(S)). Using Gabber's theory of prime-to-l alterations and the deformation theory of twisted sheaves, we prove that ind(alpha) vertical bar per(alpha) 4 for alpha of period prime to 6p, giving the first uniform period-index bounds over such fields.
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作者：Guo, Shaoming; Zhang, Ruixiang
作者单位：Institute for Advanced Study - USA; Indiana University System; Indiana University Bloomington; University of Wisconsin System; University of Wisconsin Madison
摘要：We prove a sharp upper bound on the number of integer solutions of the Parsell-Vinogradov system in every dimension d >= 2
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作者：Kontsevich, Maxim; Tschinkel, Yuri
作者单位：Universite Paris Saclay; New York University; Simons Foundation
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作者：Gutierrez-Romo, Rodolfo
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We classify the Rauzy-Veech groups of all connected components of all strata of the moduli space of translation surfaces in absolute homology, showing, in particular, that they are commensurable to arithmetic lattices of symplectic groups. As a corollary, we prove a conjecture of Zorich about the Zariski-density of such groups.
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作者：Bruned, Y.; Hairer, M.; Zambotti, L.
作者单位：Imperial College London; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
摘要：We give a systematic description of a canonical renormalisation procedure of stochastic PDEs containing nonlinearities involving generalised functions. This theory is based on the construction of a new class of regularity structures which comes with an explicit and elegant description of a subgroup of their group of automorphisms. This subgroup is sufficiently large to be able to implement a version of the BPHZ renormalisation prescription in this context. This is in stark contrast to previous...
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作者：Astorg, Matthieu; Gauthier, Thomas; Mihalache, Nicolae; Vigny, Gabriel
作者单位：Universite de Orleans; Universite de Picardie Jules Verne (UPJV); Universite Paris Saclay; Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：The moduli space M-d of degree d >= 2 rational maps can naturally be endowed with a measure mu(bif) detecting maximal bifurcations, called the bifurcation measure. We prove that the support of the bifurcation measure mu bif has positive Lebesgue measure. To do so, we establish a general sufficient condition for the conjugacy class of a rational map to belong to the support of mu bif and we exhibit a large set of Collet-Eckmann rational maps which satisfy this condition. As a consequence, we ge...
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作者：Wu, Sijue
作者单位：University of Michigan System; University of Michigan
摘要：We consider the two dimensional gravity water wave equation in a regime where the free interface is allowed to be non-C-1. In this regime, only a degenerate Taylor inequality -partial derivative P/partial derivative n >= 0 holds, with degeneracy at the singularities. In Kinsey and Wu (Camb J Math 6(2):93-181, 2018) an energy functional E(t) was constructed and an a-priori estimate was proved. The energy functional E(t) is not only finite for interfaces and velocities in Sobolev spaces, but als...
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作者：Saito, Takeshi
作者单位：University of Tokyo
