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作者：Sheridan, Nick; Smith, Ivan
作者单位：University of Edinburgh; University of Cambridge
摘要：We prove Kontsevich's homological mirror symmetry conjecture for certain mirror pairs arising from Batyrev-Borisov's 'dual reflexive Gorenstein cones' construction. In particular we prove HMS for all Greene-Plesser mirror pairs (i.e., Calabi-Yau hypersurfaces in quotients of weighted projective spaces). We also prove it for certain mirror Calabi-Yau complete intersections arising from Borisov's construction via dual nef partitions, and also for certain Calabi-Yau complete intersections which d...
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作者：Lewin, Mathieu; Nam, Phan Thanh; Rougerie, Nicolas
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; University of Munich; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP)
摘要：We provide a rigorous derivation of nonlinear Gibbs measures in two and three space dimensions, starting from many-body quantum systems in thermal equilibrium. More precisely, we prove that the grand-canonical Gibbs state of a large bosonic quantum system converges to the Gibbs measure of a nonlinear Schrodinger-type classical field theory, in terms of partition functions and reduced density matrices. The Gibbs measure thus describes the behavior of the infinite Bose gas at criticality, that i...
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作者：Cavalletti, Fabio; Milman, Emanuel
作者单位：International School for Advanced Studies (SISSA); Technion Israel Institute of Technology
摘要：The Lott-Sturm-Villani Curvature-Dimension condition provides a synthetic notion for ametric-measure space to have Ricci-curvature bounded from below and dimension bounded from above. We prove that it is enough to verify this condition locally: an essentially non-branching metric-measure space (X, d, m) (so that (supp(m), d) is a length-space and m( X) < infinity) verifying the local Curvature-Dimension condition CDloc( K, N) with parameters K is an element of R and N is an element of(1, infin...
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作者：Girouard, Alexandre; Lagace, Jean
作者单位：Laval University; University of London; University College London
摘要：Using methods in the spirit of deterministic homogenisation theory we obtain convergence of the Steklov eigenvalues of a sequence of domains in a Riemannian manifold to weighted Laplace eigenvalues of that manifold. The domains are obtained by removing small geodesic balls that are asymptotically densely uniformly distributed as their radius tends to zero. We use this relationship to construct manifolds that have large Steklov eigenvalues. In dimension two, and with constant weight equal to 1,...
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作者：Bjorklund, Michael; Kosloff, Zemer; Vaes, Stefaan
作者单位：Chalmers University of Technology; Hebrew University of Jerusalem; KU Leuven
摘要：We determine the Krieger type of nonsingular Bernoulli actions G curved right arrow Pi(g is an element of G)({0,1},mu(g)). When G is abelian, we do this for arbitrary marginal measures mu(g). We prove in particular that the action is never of type II infinity if G is abelian and not locally finite, answering Krengel's question for G=Z. When G is locally finite, we prove that type II infinity does arise. For arbitrary countable groups, we assume that the marginal measures stay away from 0 and 1...
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作者：Darbinyan, Arman
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：We show the existence of finitely presented torsion-free groups with decidable word problem that cannot be embedded in any finitely generated group with decidable conjugacy problem. This answers a well-known question of Collins from the early 1970's.
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作者：Paolini, Giovanni; Salvetti, Mario
作者单位：University of Fribourg; California Institute of Technology; University of Pisa
摘要：We prove the K(pi,1) conjecture for affine Artin groups: the complexified complement of an affine reflection arrangement is a classifying space. This is a long-standing problem, due to Arnol'd, Pham, and Thom. Our proof is based on recent advancements in the theory of dual Coxeter and Artin groups, as well as on several new results and constructions. In particular: we show that all affine noncrossing partition posets are EL-shellable; we use these posets to construct finite classifying spaces ...
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作者：Chen, Dawei; Moeller, Martin; Sauvaget, Adrien; Zagier, Don
作者单位：Boston College; Goethe University Frankfurt; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); CY Cergy Paris Universite
摘要：A Correction to this paper has been published: https://doi.org/10.1007/s00222-020-00969-4
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作者：Castro, A.; Cordoba, D.; Faraco, D.
作者单位：Autonomous University of Madrid; Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencias Matematicas (ICMAT); Universidad Carlos III de Madrid; CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM); Complutense University of Madrid; Autonomous University of Madrid
摘要：We prove the existence of mixing solutions of the incompressible porous media equation for all Muskat type H-5 initial data in the fully unstable regime. The proof combines convex integration, contour dynamics and a basic calculus for non smooth semiclassical type pseudodifferential operators which is developed.
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作者：Braun, Lukas
作者单位：University of Freiburg
摘要：We prove a conjecture of Kollar stating that the local fundamental group of a klt singularity x is finite. In fact, we prove a stronger statement, namely that the fundamental group of the smooth locus of a neighbourhood of x is finite. We call this the regional fundamental group. As the proof goes via a local-to-global induction, we simultaneously confirm finiteness of the orbifold fundamental group of the smooth locus of a weakly Fano pair.
