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作者：Subag, Eliran
摘要：We analyze the statics for pure p-spin spherical spin glass models with p >= 3, at low enough temperature. With F-N,(beta) denoting the free energy, we compute the (logarithmic) second order term of NFN,(beta) and prove that, for an appropriate centering c(N),(beta), NFN,(beta) - c(N),beta is a tight sequence. We further establish the absence of temperature chaos. Those results follow from the following geometric picture we prove for the Gibbs measure, of interest by itself: asymptotically, th...
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作者：Breuil, Christophe; Hellmann, Eugen; Schraen, Benjamin
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; University of Munster; Institut Polytechnique de Paris; Ecole Polytechnique; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：Let p be a prime number and f an overconvergent p-adic automorphic form on a definite unitary group which is split at p. Assume that f is of classical weight and that its Galois representation is crystalline at p, then f is conjectured to be a classical automorphic form. We prove new cases of this conjecture in arbitrary dimensions by making crucial use of the patched eigenvariety constructed in Breuil et al. (Math. Ann. 2016).
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作者：Beiglboeck, Mathias; Cox, Alexander M. G.; Huesmann, Martin
作者单位：Technische Universitat Wien; University of Bath; University of Bonn
摘要：The Skorokhod embedding problem is to represent a given probability as the distribution of Brownian motion at a chosen stopping time. Over the last 50 years this has become one of the important classical problems in probability theory and a number of authors have constructed solutions with particular optimality properties. These constructions employ a variety of techniques ranging from excursion theory to potential and PDE theory and have been used in many different branches of pure and applie...
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作者：Spenko, Spela; Van den Bergh, Michel
作者单位：Vrije Universiteit Brussel; Hasselt University
摘要：In this paper we generalize standard results about non-commutative resolutions of quotient singularities for finite groups to arbitrary reductive groups. We show in particular that quotient singularities for reductive groups always have non-commutative resolutions in an appropriate sense. Moreover we exhibit a large class of such singularities which have (twisted) non-commutative crepant resolutions. We discuss a number of examples, both new and old, that can be treated using our methods. Nota...
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作者：Geiss, Christof; Leclerc, Bernard; Schroeer, Jan
作者单位：Universidad Nacional Autonoma de Mexico; Universite de Caen Normandie; Centre National de la Recherche Scientifique (CNRS); Institut Universitaire de France; University of Bonn
摘要：We introduce and study a class of Iwanaga-Gorenstein algebras defined via quivers with relations associated with symmetrizable Cartan matrices. These algebras generalize the path algebras of quivers associated with symmetric Cartan matrices. We also define a corresponding class of generalized preprojective algebras. For these two classes of algebras we obtain generalizations of classical results of Gabriel, Dlab-Ringel, and Gelfand-Ponomarev. In particular, we obtain new representation theoret...
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作者：Bergeron, Nicolas; Li, Zhiyuan; Millson, John; Moeglin, Colette
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Fudan University; University System of Maryland; University of Maryland College Park; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
摘要：We prove the Noether-Lefschetz conjecture on the moduli space of quasi-polarized K3 surfaces. This is deduced as a particular case of a general theorem that states that low degree cohomology classes of arithmetic manifolds of orthogonal type are dual to the classes of special cycles, i.e. sub-arithmetic manifolds of the same type. For compact manifolds this was proved in [3], here we extend the results of [3] to non-compact manifolds. This allows us to apply our results to the moduli spaces of...
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作者：Liu, Ruochuan; Zhu, Xinwen
作者单位：Peking University; California Institute of Technology
摘要：We construct a functor from the category of p-adic ,tale local systems on a smooth rigid analytic variety X over a p-adic field to the category of vector bundles with an integrable connection on its base change to , which can be regarded as a first step towards the sought-after p-adic Riemann-Hilbert correspondence. As a consequence, we obtain the following rigidity theorem for p-adic local systems on a connected rigid analytic variety: if the stalk of such a local system at one point, regarde...
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作者：Botvinnik, Boris; Ebert, Johannes; Randal-Williams, Oscar
作者单位：University of Oregon; University of Munster; University of Cambridge
摘要：We study the homotopy type of the space of metrics of positive scalar curvature on high-dimensional compact spin manifolds. Hitchin used the fact that there are no harmonic spinors on a manifold with positive scalar curvature to construct a secondary index map from the space of positive scalar metrics to a suitable space from the real K-theory spectrum. Our main results concern the nontriviality of this map. We prove that for 2n >= 6, the natural KO-orientation from the infinite loop space of ...
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作者：He, Hongyu
作者单位：Louisiana State University System; Louisiana State University
摘要：In this paper, we give a proof of the Gan-Gross-Prasad conjecture for the discrete series of U(p, q). There are three themes in this paper: branching laws of a small A(q) (lambda) branching laws of discrete series and inductive construction of discrete series. These themes are linked together by a reciprocity law and the notion of invariant tensor product.
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作者：Casals, Roger; Luis Perez, Jose; del Pino, Alvaro; Presas, Francisco
作者单位：Massachusetts Institute of Technology (MIT); Autonomous University of Madrid; Universidad Carlos III de Madrid; Complutense University of Madrid; Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencias Matematicas (ICMAT); CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM)
摘要：In this article we prove that the inclusion of the space of Engel structures of a smooth 4-manifold into the space of full flags of its tangent bundle induces surjections in all homotopy groups. In particular, we construct Engel structures representing any given full flag.
