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作者：Cekic, Mihajlo; Delarue, Benjamin; Dyatlov, Semyon; Paternain, Gabriel P.
作者单位：University of Zurich; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; University of Paderborn; Massachusetts Institute of Technology (MIT); University of Cambridge
摘要：We show that for a generic conformal metric perturbation of a compact hyperbolic 3-manifold Sigma with Betti number b(1), the order of vanishing of the Ruelle zeta function at zero equals 4 - b(1), while in the hyperbolic case it is equal to 4 - 2b(1). This is in contrast to the 2-dimensional case where the order of vanishing is a topological invariant. The proof uses the microlocal approach to dynamical zeta functions, giving a geometric description of generalized Pollicott-Ruelle resonant di...
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作者：Maulik, Davesh; Shankar, Ananth N.; Tang, Yunqing
作者单位：Massachusetts Institute of Technology (MIT); University of Wisconsin System; University of Wisconsin Madison; Princeton University
摘要：Let X -> C be a non-isotrivial and generically ordinary family of K3 surfaces over a proper curve C in characteristic p >= 5. We prove that the geometric Picard rank jumps at infinitely many closed points of C. More generally, suppose that we are given the canonical model of a Shimura variety S of orthogonal type, associated to a lattice of signature (b, 2) that is self-dual at p. We prove that any generically ordinary proper curve C in S-(F) over barp intersects special divisors of S-(F) over...
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作者：Alexakis, Spyros; Feizmohammadi, Ali; Oksanen, Lauri
作者单位：University of Toronto; University of London; University College London
摘要：We introduce a method of solving inverse boundary value problems for wave equations on Lorentzian manifolds, and show that zeroth order coefficients can be recovered under certain curvature bounds. The set of Lorentzian metrics satisfying the curvature bounds has a non-empty interior in the sense of arbitrary, smooth perturbations of the metric, whereas all previous results on this problem impose conditions on the metric that force it to be real analytic with respect to a suitably defined time...
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作者：Feng, Tony; Galatius, Soren; Venkatesh, Akshay
作者单位：University of California System; University of California Berkeley; University of Copenhagen; Institute for Advanced Study - USA
摘要：We study a symplectic variant of algebraic K-theory of the integers, which comes equipped with a canonical action of the absolute Galois group of Q. We compute this action explicitly. The representations we see are extensions of Tate twists Z(p)(2k - 1) by a trivial representation, and we characterize them by a universal property among such extensions. The key tool in the proof is the theory of complex multiplication for abelian varieties.
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作者：Shelukhin, Egor
作者单位：Universite de Montreal
摘要：We prove a conjecture of Viterbo from 2007 on the existence of a uniform bound on the Lagrangian spectral norm of Hamiltonian deformations of the zero section in unit cotangent disk bundles, for bases given by compact rank one symmetric spaces S-n,RPn,CPn,HPn,n >= 1. We discuss generalizations and give applications, in particular to C0 symplectic topology. Our key method consists in a quantitative deformation argument for Floer persistence modules that allows to excise a divisor.
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作者：Banks, Peter; Panzer, Erik; Pym, Brent
作者单位：University of Oxford; University of Edinburgh; McGill University
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作者：Merle, Frank; Raphael, Pierre; Rodnianski, Igor; Szeftel, Jeremie
作者单位：CY Cergy Paris Universite; Princeton University; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Sorbonne Universite; Universite Paris Cite
摘要：We consider the energy supercritical defocusing nonlinear Schrodinger equation i partial derivative(t)u + Delta u - u vertical bar u vertical bar(p-1) = 0 in dimension d >= 5. In a suitable range of energy supercritical parameters (d, p), we prove the existence of C-infinity well localized spherically symmetric initial data such that the corresponding unique strong solution blows up in finite time. Unlike other known blowup mechanisms, the singularity formation does not occur by concentration ...
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作者：Dolgopyat, Dmitry; Dong, Changguang; Kanigowski, Adam; Nandori, Peter
作者单位：University System of Maryland; University of Maryland College Park; Yeshiva University; Nankai University; Nankai University
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作者：Beentjes, Sjoerd Viktor; Calabrese, John; Rennemo, Jorgen Vold
作者单位：University of Edinburgh; Heriot Watt University; University of Edinburgh; University of Oslo
摘要：We prove the crepant resolution conjecture for Donaldson-Thomas invariants of hard Lefschetz 3-Calabi-Yau (CY3) orbifolds, formulated by Bryan-Cadman-Young, interpreting the statement as an equality of rational functions. In order to do so, we show that the generating series of stable pair invariants on any CY3 orbifold is the expansion of a rational function. As a corollary, we deduce a symmetry of this function induced by the derived dualising functor. Our methods also yield a proof of the o...
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作者：Corvaja, Pietro; Rapinchuk, Andrei S.; Ren, Jinbo; Zannier, Umberto M.
作者单位：University of Virginia; Scuola Normale Superiore di Pisa
摘要：We prove that if a linear group Gamma subset of GL(n)(K) over a field K of characteristic zero is boundedly generated by semi-simple (diagonalizable) elements then it is virtually solvable. As a consequence, one obtains that infinite S-arithmetic subgroups of absolutely almost simple anisotropic algebraic groups over number fields are never boundedly generated. Our proof relies on Laurent's theorem from Diophantine geometry and properties of generic elements.
