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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; Vilonen, Kari
作者单位：Massachusetts Institute of Technology (MIT); University of Melbourne; University of Helsinki
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作者：Zhuang, Ziquan
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We give an algebraic proof of the equivalence of equivariant K-semistability (resp. equivariant K-polystability) with geometric K-semistability (resp. geometric K-polystability). Along the way we also prove the existence and uniqueness of minimal optimal destabilizing centers on K-unstable log Fano pairs.
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作者：Budur, Nero; van der Veer, Robin; Wu, Lei; Zhou, Peng
作者单位：KU Leuven; Utah System of Higher Education; University of Utah; Universite Paris Saclay
摘要：We prove a conjecture of the first author relating the Bernstein-Sato ideal of a finite collection of multivariate polynomials with cohomology support loci of rank one complex local systems. This generalizes a classical theorem of Malgrange and Kashiwara relating the b-function of a multivariate polynomial with the monodromy eigenvalues on the Milnor fibers cohomology.
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作者：Hedden, Matthew; Pinzon-Caicedo, Juanita
作者单位：Michigan State University; University of Notre Dame
摘要：We conjecture that satellite operations are either constant or have infinite rank in the concordance group. We reduce this to the difficult case of winding number zero satellites, and use SO(3) gauge theory to provide a general criterion sufficient for the image of a satellite operation to generate an infinite rank subgroup of the smooth concordance group C. Our criterion applies widely; notably to many unknotted patterns for which the corresponding operators on the topological concordance gro...
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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：Karpukhin, Mikhail
作者单位：University of California System; University of California Irvine
摘要：In the present paper we use twistor theory in order to solve two problems related to harmonic maps from surfaces to Euclidean spheres Sn. First, we propose a new approach to isoperimetric eigenvalue inequalities based on energy index. Using this approach we show that for any positive k, the k-th non-zero eigenvalue of the Laplacian on the real projective plane endowed with a metric of unit area, is maximized on the sequence of metrics converging to a union of (k - 1) identical copies of round ...
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作者：Blanco, Guillem
作者单位：KU Leuven
摘要：We present a proof of a conjecture proposed by Yano (Sci Rep Saitama Univ Ser 10(2): 21-28, 1982) about the generic b-exponents of irreducible plane curve singularities.
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作者：Beraldo, Dario
作者单位：University of London; University College London
摘要：We characterize the tempered part of the automorphic Langlands category D(Bun(G)) using the geometry of the big cell in the affine Grassmannian. We deduce that, for G non-abelian, tempered D-modules have no de Rham cohomology with compact support. The latter fact boils down to a concrete statement, which we prove using the Ran space and some explicit t-structure estimates: for G non-abelian and Sigma a smooth affine curve, the Borel-Moore homology of the indscheme Maps(Sigma, G) vanishes.
