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作者：Tiozzo, Giulio
作者单位：Yale University
摘要：The core entropy of polynomials, recently introduced by W. Thurston, is a dynamical invariant which can be defined purely in combinatorial terms, and provides a useful tool to study parameter spaces of polynomials. The theory of core entropy extends the entropy theory for real unimodal maps to complex polynomials: the real segment is replaced by an invariant tree, known as the Hubbard tree, which lies inside the filled Julia set. We prove that the core entropy of quadratic polynomials varies c...
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作者：Bayer, Arend; Macri, Emanuele; Stellari, Paolo
作者单位：University of Edinburgh; University of Edinburgh; Heriot Watt University; University System of Ohio; Ohio State University; Northeastern University; University of Milan
摘要：We describe a connected component of the space of stability conditions on abelian threefolds, and on Calabi-Yau threefolds obtained as (the crepant resolution of) a finite quotient of an abelian threefold. Our proof includes the following essential steps:We simultaneously strengthen a conjecture by the first two authors and Toda, and prove that it follows from a more natural and seemingly weaker statement. This conjecture is a Bogomolov-Gieseker type inequality involving the third Chern charac...
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作者：Rouquier, Raphael; Shan, Peng; Varagnolo, Michela; Vasserot, Eric
作者单位：University of California System; University of California Los Angeles; Universite Paris Saclay; CY Cergy Paris Universite; Universite Paris Cite
摘要：Varagnolo and Vasserot conjectured an equivalence between the category for CRDAHA's and a subcategory of an affine parabolic category O of type A. We prove this conjecture. As applications, we prove a conjecture of Rouquier on the dimension of simple modules of CRDAHA's and a conjecture of Chuang-Miyachi on the Koszul duality for the category of CRDAHA's.
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作者：Venerucci, Rodolfo
作者单位：University of Duisburg Essen
摘要：Let A/Q be an elliptic curve with split multiplicative reduction at a prime p. We prove (an analogue of) a conjecture of Perrin-Riou, relating p-adic Beilinson-Kato elements to Heegner points in A(Q), and a large part of the rank-one case of the Mazur-Tate-Teitelbaum exceptional zero conjecture for the cyclotomic p-adic L-function of A. More generally, let f be the weight-two newform associated with A, let f(infinity) be the Hida family of f, and let L p(f(infinity), k, s) be the Mazur-Kitagaw...
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作者：Carlotto, Alessandro; Chodosh, Otis; Eichmair, Michael
作者单位：University of Cambridge; University of Vienna
摘要：The study of stable minimal surfaces in Riemannian 3-manifolds (M, g) with non-negative scalar curvature has a rich history. In this paper, we prove rigidity of such surfaces when (M, g) is asymptotically flat and has horizon boundary. As a consequence, we obtain an effective version of the positive mass theorem in terms of isoperimetric or, more generally, closed volume-preserving stable CMC surfaces that is appealing from both a physical and a purely geometric point of view. We also include ...
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作者：Liu, Yifeng
作者单位：Northwestern University
摘要：Let E be an elliptic curve over and A another elliptic curve over a real quadratic number field. We construct a -motive of rank 8, together with a distinguished class in the associated Bloch-Kato Selmer group, using Hirzebruch-Zagier cycles, that is, graphs of Hirzebruch-Zagier morphisms. We show that, under certain assumptions on E and A, the non-vanishing of the central critical value of the (twisted) triple product L-function attached to (E, A) implies that the dimension of the associated B...
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作者：Maulik, Davesh
作者单位：Columbia University
摘要：Given a planar curve singularity, we prove a conjecture of Oblomkov-Shende, relating the geometry of its Hilbert scheme of points to the HOMFLY polynomial of the associated algebraic link. More generally, we prove an extension of this conjecture, due to Diaconescu-Hua-Soibelman, relating stable pair invariants on the conifold to the colored HOMFLY polynomial of the algebraic link. Our proof uses wall-crossing techniques to prove a blowup identity on the algebro-geometric side. We prove a match...
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作者：Carlotto, Alessandro; Schoen, Richard
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of California System; University of California Irvine
摘要：We perform an optimal localization of asymptotically flat initial data sets and construct data that have positive ADM mass but are exactly trivial outside a cone of arbitrarily small aperture. The gluing scheme that we develop allows to produce a new class of N-body solutions for the Einstein equation, which patently exhibit the phenomenon of gravitational shielding: for any large T we can engineer solutions where any two massive bodies do not interact at all for any time , in striking contras...
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作者：Hakavuori, Eero; Le Donne, Enrico
作者单位：University of Jyvaskyla
摘要：We give a short solution to one of the main open problems in subriemannian geometry. Namely, we prove that length minimizers do not have corner-type singularities. With this result we solve Problem II of Agrachev's list, and provide the first general result toward the 30-year-old open problem of regularity of subriemannian geodesics.
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作者：Bernstein, Jacob; Wang, Lu
作者单位：Johns Hopkins University; University of Wisconsin System; University of Wisconsin Madison
摘要：The entropy is a natural geometric quantity which measures the complexity of a hypersurface in . It is non-increasing along the mean curvature flow and so plays a significant role in analyzing the dynamics of this flow. In (Colding et al., J Differ Geom 95(1):53-69, 2013), Colding-Ilmanen-Minicozzi-White showed that within the class of closed smooth self-shrinking solutions of the mean curvature flow in , the entropy is uniquely minimized at the round sphere. They conjectured that, for , the r...
