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作者：Wang, Zhiren
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We show that the Mobius function is disjoint to every analytic skew product dynamical system on over a rotation of the circle.
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作者：Boutonnet, Remi; Ioana, Adrian; Golsefidy, Alireza Salehi
作者单位：Centre National de la Recherche Scientifique (CNRS); Inria; Universite de Bordeaux; University of California System; University of California San Diego
摘要：We introduce a novel notion of local spectral gap for general, possibly infinite, measure preserving actions. We establish local spectral gap for the left translation action , whenever is a dense subgroup generated by algebraic elements of an arbitrary connected simple Lie group G. This extends to the non-compact setting works of Bourgain and Gamburd (Invent Math 171:83-121, 2008; J Eur Math Soc (JEMS) 14:1455-1511, 2012), and Benoist and de Saxc, (Invent Math 205:337-361, 2016). We present se...
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作者：Caffarelli, Luis; Ros-Oton, Xavier; Serra, Joaquim
作者单位：University of Texas System; University of Texas Austin; Universitat Politecnica de Catalunya
摘要：We study the obstacle problem for integro-differential operators of order 2s, with s is an element of(0,1). Our main results establish the optimal C<^>{1,s} regularity of solutions u, and the C<^>{1,\alpha} regularity of the free boundary near regular points. Namely, we prove the following dichotomy at all free boundary points x_0\in\partial\{u=\varphi\}: (i) either u(x)-\varphi(x)=c\,d<^>{1+s}(x)+o(|x-x_0|<^>{1+s+\alpha}) for some c>0, (ii) or u(x)-\varphi(x)=o(|x-x_0|<^>{1+s+\alpha}), where ...
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作者：Sam, Steven V.
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：Over a field of characteristic zero, we prove that for each r, there exists a constant C(r) so that the prime ideal of the rth secant variety of any Veronese embedding of any projective space is generated by polynomials of degree at most C(r). The main idea is to consider the coordinate ring of all of the ambient spaces of the Veronese embeddings at once by endowing it with the structure of a Hopf ring, and to show that its ideals are finitely generated. We also prove a similar statement for p...
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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...
