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• Unique Cartan decomposition for II1 factors arising from arbitrary actions of free groups AI翻译
  作者：Popa, Sorin; Vaes, Stefaan
  作者单位：University of California System; University of California Los Angeles; KU Leuven
  摘要：We prove that for any free ergodic probability measure-preserving action of a free group on n generators , the associated group measure space II1 factor has L (a)(X) as its unique Cartan subalgebra, up to unitary conjugacy. We deduce that group measure space II1 factors arising from actions of free groups with different number of generators are never isomorphic. We actually prove unique Cartan decomposition results for II1 factors arising from arbitrary actions of a much larger family of group...
• Every finite group is the group of self-homotopy equivalences of an elliptic space AI翻译
  作者：Costoya, Cristina; Viruel, Antonio
  作者单位：Universidad de Malaga; Universidade da Coruna; Universidad de Malaga
  摘要：We prove that every finite group G can be realized as the group of self-homotopy equivalences of infinitely many elliptic spaces X. To construct those spaces we introduce a new technique which leads, for example, to the existence of infinitely many inflexible manifolds. Further applications to representation theory will appear in a separate paper.
• Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton AI翻译
  作者：Martel, Yvan; Merle, Frank; Raphael, Pierre
  作者单位：Universite Paris Saclay; Institut Universitaire de France; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); CY Cergy Paris Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Universitaire de France
  摘要：We consider the quintic generalized Korteweg-de Vries equation (gKdV) which is a canonical mass critical problem, for initial data in H (1) close to the soliton. In earlier works on this problem, finite- or infinite-time blow up was proved for non-positive energy solutions, and the solitary wave was shown to be the universal blow-up profile, see [16], [26] and [20]. For well-localized initial data, finite-time blow up with an upper bound on blow-up rate was obtained in [18]. In this paper, we ...
• Geometric quantization for proper moment maps: the Vergne conjecture AI翻译
  作者：Ma, Xiaonan; Zhang, Weiping
  作者单位：Universite Paris Cite; Nankai University; Nankai University
  摘要：We establish an analytic interpretation for the index of certain transversally elliptic symbols on non-compact manifolds. By using this interpretation, we establish a geometric quantization formula for a Hamiltonian action of a compact Lie group acting on a non-compact symplectic manifold with proper moment map. In particular, we present a solution to a conjecture of MichSle Vergne in her ICM 2006 plenary lecture.
• K-homology and index theory on contact manifolds AI翻译
  作者：Baum, Paul F.; van Erp, Erik
  作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Dartmouth College
  摘要：This paper applies K-homology to solve the index problem for a class of hypoelliptic (but not elliptic) operators on contact manifolds. K-homology is the dual theory to K-theory. We explicitly calculate the K-cycle (i.e., the element in geometric K-homology) determined by any hypoelliptic Fredholm operator in the Heisenberg calculus. The index theorem of this paper precisely indicates how the analytic versus geometric K-homology setting provides an effective framework for extending formulas of...
• Square-free values of f(p), f cubic AI翻译
  作者：Helfgott, Harald Andres
  作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS)
  摘要：Let , . Assume that f does not have repeated roots. Assume as well that, for every prime q, mod q (2) has at least one solution in . Then, under these two necessary conditions, there are infinitely many primes p such that f(p) is square-free.
• Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry AI翻译
  作者：Donaldson, Simon; Sun, Song
  作者单位：Imperial College London
  摘要：We prove a general result about the geometry of holomorphic line bundles over Kahler manifolds.
• Rigidity around Poisson submanifolds AI翻译
  作者：Marcut, Ioan
  作者单位：University of Illinois System; University of Illinois Urbana-Champaign
  摘要：We prove a rigidity theorem in Poisson geometry around compact Poisson submanifolds, using the Nash-Moser fast convergence method. In the case of one-point submanifolds (fixed points), this implies a stronger version of Conn's linearization theorem [2], also proving that Conn's theorem is a manifestation of a rigidity phenomenon; similarly, in the case of arbitrary symplectic leaves, it gives a stronger version of the local normal form theorem [7]. We can also use the rigidity theorem to compu...
• A sharp lower bound for the log canonical threshold AI翻译
  作者：Demailly, Jean-Pierre; Hoang Hiep Pham
  作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Hanoi National University of Education
  摘要：In this note, we prove a sharp lower bound for the log canonical threshold of a plurisubharmonic function with an isolated singularity at 0 in an open subset of . This threshold is defined as the supremum of constants c > 0 such that is integrable on a neighborhood of 0. We relate to the intermediate multiplicity numbers , defined as the Lelong numbers of at 0 (so that in particular ). Our main result is that . This inequality is shown to be sharp; it simultaneously improves the classical resu...