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作者：Bader, Uri; Boutonnet, Remi; Houdayer, Cyril; Peterson, Jesse
作者单位：Weizmann Institute of Science; Universite de Bordeaux; Universite Paris Saclay; Vanderbilt University
摘要：We discuss special properties of the spaces of characters and positive definite functions, as well as their associated dynamics, for arithmetic groups of product type. Axiomatizing these properties, we define the notions of charmenability and charfiniteness and study their applications to the topological dynamics, ergodic theory and unitary representation theory of the given groups. To do that, we study singularity properties of equivariant normal ucp maps between certain von Neumann algebras....
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作者：da Silva, A. Belotto; Figalli, A.; Parusinski, A.; Rifford, L.
作者单位：Aix-Marseille Universite; Universite Paris Cite; Sorbonne Universite; Swiss Federal Institutes of Technology Domain; ETH Zurich; Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Universite Cote d'Azur; Inria; Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper we prove the strong Sard conjecture for sub-Riemannian structures on 3-dimensional analytic manifolds. More precisely, given a totally nonholonomic analytic distribution of rank 2 on a 3-dimensional analytic manifold, we investigate the size of the set of points that can be reached by singular horizontal paths starting from a given point and prove that it has Hausdorff dimension at most 1. In fact, provided that the lengths of the singular curves under consideration are bounded w...
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作者：Ko, Hyerim; Lee, Sanghyuk; Oh, Sewook
作者单位：Seoul National University (SNU)
摘要：Let M be the maximal operator associated to a smooth curve in R-3 which has nonvanishing curvature and torsion. We prove that M is bounded on L-p if and only if p > 3.
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作者：Bahouri, Hajer; Perelman, Galina
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：This paper is dedicated to the study of the derivative nonlinear Schrodinger equation on the real line. The local well-posedness of this equation in the Sobolev spaces H-s(R) is well understood since a couple of decades, while the global well-posedness is not completely settled. For the latter issue, the best known results up-to-date concern either Cauchy data in H-1/2(R) with mass strictly less than 4 pi or general initial conditions in the weighted Sobolev space H-2,H-2(R) . In this article,...
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作者：Bonnaillie-Noel, Virginie; Herau, Frederic; Raymond, Nicolas
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Nantes Universite; Universite d'Angers
摘要：The magnetic Schrodinger operator, with Neumann boundary condition, on a smooth, bounded, and simply connected domain Omega of the Euclidean plane is considered in the semiclassical limit. When Omega has a symmetry axis, the semiclassical splitting of the first two eigenvalues is analyzed. The first explicit tunneling formula in a pure magnetic field is established. The analysis is based on a pseudo-differential reduction to the boundary and the proof of the first known optimal purely magnetic...
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作者：Li, Chi
作者单位：Purdue University System; Purdue University; Rutgers University System; Rutgers University New Brunswick
摘要：Let X be any Q-Fano variety and Aut(X)(0) be the identity component of the automorphism group of X. Let G be a connected reductive subgroup of Aut(X)(0) that contains a maximal torus of Aut(X)(0). We prove that X admits a Kahler-Einstein metric if and only if X is G-uniformly K-stable. This proves a version of Yau-Tian-Donaldson conjecture for arbitrary singular Fano varieties. A key new ingredient is a valuative criterion for G-uniform K-stability.
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作者：De Marchis, Francesca; Malchiodi, Andrea; Martinazzi, Luca; Thizy, Pierre-Damien
作者单位：Sapienza University Rome; Scuola Normale Superiore di Pisa; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：Given a closed Riemann surface (Sigma, g(0)) and any positive weight f is an element of C-infinity(Sigma), we use a minmax scheme together with compactness, quantization results and with sharp energy estimates to prove the existence of positive critical points of the functional I-p,I-beta(u) = 2 - p/2 (p parallel to u parallel to(2)(H1)/2 beta) p/2-p - in integral(Sigma)(e(up-) - 1) f d v(g0), for every p is an element of (1, 2) and beta > 0, or for p = 1 and beta is an element of (0, infinity...
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作者：Hausel, Tamas; Hitchin, Nigel
作者单位：Institute of Science & Technology - Austria; University of Oxford
摘要：We define and study the existence of very stable Higgs bundles on Riemann surfaces, how it implies a precise formula for the multiplicity of the very stable components of the global nilpotent cone and its relationship to mirror symmetry. Themain ingredients are the Bialynicki-Birula theory of C*-actions on semiprojective varieties, C* characters of indices of C*-equivariant coherent sheaves, Hecke transformation for Higgs bundles, relative Fourier-Mukai transform along the Hitchin fibration, h...
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作者：Nguyen, Hoi H.; Wood, Melanie Matchett
作者单位：University System of Ohio; Ohio State University; University of Wisconsin System; University of Wisconsin Madison
摘要：For a random matrix of entries sampled independently from a fairly general distribution in Z we study the probability that the cokernel is isomorphic to a given finite abelian group, or when it is cyclic. This includes the probability that the linear map between the integer lattices given by the matrix is surjective. We show that these statistics are asymptotically universal (as the size of the matrix goes to infinity), given by precise formulas involving zeta values, and agree with distributi...
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作者：Luckhaus, Stephan; Zemas, Konstantinos
作者单位：Leipzig University; University of Munster
摘要：We investigate both linear and nonlinear stability aspects of rigid motions (resp. Mobius transformations) of Sn-1 among Sobolev maps from Sn-1 into R-n. Unlike similar in flavour results for maps defined on domains of R-n and mapping into R-n, not only an isometric (resp. conformal) deficit is necessary in this more flexible setting, but also a deficit measuring the distortion of Sn-1 under the maps in consideration. The latter is defined as an associated isoperimetric type of deficit. The fo...
