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作者：Ascher, Kenneth; DeVleming, Kristin; Liu, Yuchen
作者单位：University of California System; University of California Irvine; University of Massachusetts System; University of Massachusetts Amherst; Northwestern University
摘要：We show that the K-moduli spaces of log Fano pairs (P-3, cS) where S is a quartic surface interpolate between the GIT moduli space of quartic surfaces and the Baily-Borel compactification of moduli of quartic K3 surfaces as c varies in the interval (0, 1). We completely describe the wall crossings of these K-moduli spaces. As the main application, we verify Laza-O' Grady's prediction on the Hassett-Keel-Looijenga program for quartic K3 surfaces. We also obtain the K-moduli compactification of ...
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作者：Topley, Lewis
作者单位：University of Bath
摘要：In this paper we study the variety of one dimensional representations of a finite W algebra attached to a classical Lie algebra, giving a precise description of the dimensions of the irreducible components. We apply this to prove a conjecture of Losev describing the image of his orbit method map. In order to do so we first establish new Yangian-type presentations of semiclassical limits of the W-algebras attached to distinguished nilpotent elements in classical Lie algebras, using Dirac reduct...
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作者：He, Qiao; Li, Chao; Shi, Yousheng; Yang, Tonghai
作者单位：University of Wisconsin System; University of Wisconsin Madison; Columbia University; Zhejiang University
摘要：We prove the Kudla-Rapoport conjecture for Kramer models of unitary Rapoport-Zink spaces at ramified places. It is a precise identity between arithmetic intersection numbers of special cycles on Kramer models and modified derived local densities of hermitian forms. As an application, we relax the local assumptions at ramified places in the arithmetic Siegel-Weil formula for unitary Shimura varieties, which is in particular applicable to unitary Shimura varieties associated to unimodular hermit...
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作者：Labourie, Francois; Toulisse, Jeremy
作者单位：Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
摘要：We study in this paper quasiperiodic maximal surfaces in pseudo-hyperbolic spaces and show that they are characterised by a curvature condition, Gromov hyperbolicity or conformal hyperbolicity. We show that the limit curves of these surfaces in the Einstein Universe admits a canonical quasisymmetric parametrisation, while conversely every quasisymmetric curve in the Einstein Universe bounds a quasiperiodic surface in such a way that the quasisymmetric parametrisation is a continuous extension ...
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作者：Li, Jialun; Pan, Wenyu
作者单位：University of Zurich; University of Chicago
摘要：Let Gamma be a geometrically finite discrete subgroup in SO(d + 1, 1)degrees with parabolic elements. We establish exponential mixing of the geodesic flow on the unit tangent bundle T-1 (Gamma\Hd+1) with respect to the Bowen-Margulis- Sullivan measure, which is the unique probability measure on T-1 (Gamma\Hd+1) with maximal entropy. As an application, we obtain a resonance-free region for the resolvent of the Laplacian on Gamma\Hd+1. Our approach is to construct a coding for the geodesic flow ...
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作者：Bright, Martin; Newton, Rachel
作者单位：University of London; King's College London
摘要：Classifying elements of the Brauer group of a variety X over a p-adic field by the p-adic accuracy needed to evaluate them gives a filtration on Br X. We relate this filtration to that defined by Kato's Swan conductor. The refined Swan conductor con-trols how the evaluation maps vary on p-adic discs: this provides a geometric char-acterisation of the refined Swan conductor. We give applications to rational points on varieties over number fields, including failure of weak approximation for vari...
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作者：Gunningham, Sam; Jordan, David; Safronov, Pavel
作者单位：Montana State University System; Montana State University Bozeman; University of Edinburgh; University of Zurich
摘要：We give a new, algebraically computable formula for skein modules of closed 3-manifolds via Heegaard splittings. As an application, we prove that skein modules of closed 3-manifolds are finite-dimensional, resolving in the affirmative a conjecture of Witten.
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作者：Banks, William; Ford, Kevin; Tao, Terence
作者单位：University of Missouri System; University of Missouri Columbia; University of Illinois System; University of Illinois Urbana-Champaign; University of California System; University of California Los Angeles
摘要：We introduce a new probabilistic model of the primes consisting of integers that survive the sieving process when a random residue class is selected for every prime modulus below a specific bound. From a rigorous analysis of this model, we obtain heuristic upper and lower bounds for the size of the largest prime gap in the interval [1, x]. Our results are stated in terms of the extremal bounds in the interval sieve problem. The same methods also allow us to rigorously relate the validity of th...
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作者：Berti, Massimiliano; Hassainia, Zineb; Masmoudi, Nader
作者单位：International School for Advanced Studies (SISSA); New York University; New York University Abu Dhabi; New York University
摘要：We prove the existence of time quasi-periodic vortex patch solutions of the 2d-Euler equations in R2, close to uniformly rotating Kirchhoff elliptical vortices, with aspect ratios belonging to a set of asymptotically full Lebesgue measure. The problem is reformulated into a quasi-linear Hamiltonian equation for a radial displacement from the ellipse. A major difficulty of the KAM proof is the presence of a zero normal mode frequency, which is due to the conservation of the angular momentum. Th...
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作者：Ivorra, Florian; Sebag, Julien
作者单位：Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Let k be a field of characteristic zero and let X be an algebraic k-variety endowed with an action of the multiplicative algebraic monoid A(1). In this article, we prove that the nearby motivic sheaf functor of a weighted A(1)-equivariant function on X commutes with direct (and exceptional direct) images when applied to constant objects and their twists by Thom spaces of equivariant vector bundles. This proves a generalized categorified version of the conjectures of Behrend-Bryan-Szendro?i and...
