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作者：Bruinier, Jan Hendrik; Ehlen, Stephan; Yang, Tonghai
作者单位：Technical University of Darmstadt; University of Cologne; University of Wisconsin System; University of Wisconsin Madison
摘要：Gross and Zagier conjectured that the CM values (of certain Hecke translates) of the automorphic Green function G(s) (z(1), z(2)) for the elliptic modular group at positive integral spectral parameter s are given by logarithms of algebraic numbers in suitable class fields. We prove a partial average version of this conjecture, where we sum in the first variable z(1) over all CM points of a fixed discriminant d(1) (twisted by a genus character), and allow in the second variable the evaluation a...
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作者：Codogni, Giulio; Patakfalvi, Zsolt
作者单位：University of Rome Tor Vergata; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：The Chow-Mumford (CM) line bundle is a functorial line bundle on the base of any family of klt Fano varieties. It is conjectured that it yields a polarization on the moduli space of K-poly-stable klt Fano varieties. Proving ampleness of the CM line bundle boils down to showing semi-positivity/positivity statements about the CM-line bundle for families with K-semi-stable/K-polystable fibers. We prove the necessary semi-positivity statements in the K-semi-stable situation, and the necessary posi...
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作者：Hafner, Dietrich; Hintz, Peter; Vasy, Andras
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Massachusetts Institute of Technology (MIT); Stanford University
摘要：We prove the linear stability of slowly rotating Kerr black holes as solutions of the Einstein vacuum equations: linearized perturbations of a Kerr metric decay at an inverse polynomial rate to a linearized Kerr metric plus a pure gauge term. We work in a natural wave map/DeTurck gauge and show that the pure gauge term can be taken to lie in a fixed 7-dimensional space with a simple geometric interpretation. Our proof rests on a robust general framework, based on recent advances in microlocal ...
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作者：Aggarwal, Amol
作者单位：Columbia University
摘要：In this paper we analyze the large genus asymptotics for intersection numbers between psi-classes, also called correlators, on the moduli space of stable curves. Our proofs proceed through a combinatorial analysis of the recursive relations (Virasoro constraints) that uniquely determine these correlators, together with a comparison between the coefficients in these relations with the jump probabilities of a certain asymmetric simple random walk. As an application of this result, we provide the...
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作者：Bezrukavnikov, Roman; Losev, Ivan
作者单位：Massachusetts Institute of Technology (MIT); Yale University
摘要：We compute the number of finite dimensional irreducible modules for the algebras quantizing Nakajima quiver varieties. We get a lower bound for all quivers and vectors of framing. We provide an exact count in the case when the quiver is of finite type or is of affine type and the framing is the coordinate vector at the extending vertex. The latter case precisely covers Etingof's conjecture on the number of finite dimensional irreducible representations for Symplectic reflection algebras associ...
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作者：Izumi, Masaki; Matui, Hiroki
作者单位：Kyoto University; Chiba University
摘要：This is the second part of our serial work on the classification of poly-Z group actions on Kirchberg algebras. Based on technical results obtained in our previous work, we completely reduce the problem to the classification of continuous fields of Kirchberg algebras over the classifying spaces. As an application, we determine the number of cocycle conjugacy classes of outer Z(n)-actions on the Cuntz algebras.
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作者：Clausen, Dustin; Mathew, Akhil
作者单位：University of Copenhagen; University of Chicago
摘要：We study the etale sheafification of algebraic K-theory, called etale K-theory. Our main results show that etale K-theory is very close to a noncommutative invariant called Selmer K-theory, which is defined at the level of categories. Consequently, we show that etale K-theory has surprisingly well-behaved properties, integrally and without finiteness assumptions. A key theoretical ingredient is the distinction, which we investigate in detail, between sheaves and hypersheaves of spectra on etal...
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作者：Kemeny, Michael
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：We introduce a relativization of the secant sheaves from Green and Lazarsfeld (A simple proof of Petri's theorem on canonical curves, Geometry Today, 1984) and Ein and Lazarsfeld (Inventiones Math 190:603-646, 2012) and apply this construction to the study of syzygies of canonical curves. As a first application, we give a simpler proof of Voisin's Theorem for general canonical curves. This completely determines the terms of the minimal free resolution of the coordinate ring of such curves. Sec...
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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：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.
