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作者：Bowden, Jonathan; Gironella, Fabio; Moreno, Agustin
作者单位：University of Regensburg; Monash University; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Humboldt University of Berlin; University of Augsburg; Uppsala University; Institute for Advanced Study - USA
摘要：Given a contact structure on a manifold V together with a supporting open book decomposition, Bourgeois gave an explicit construction of a contact structure on V x T-2. We prove that all such structures are universally tight in dimension 5, independent of whether the original contact manifold is itself tight or overtwisted. In arbitrary dimensions, we provide obstructions to the existence of strong symplectic fillings of Bourgeois manifolds. This gives a broad class of new examples of weakly b...
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作者：Liu, Ruochuan; Wang, Guozhen
作者单位：Fudan University; Peking University
摘要：We introduce a new approach to determining the structure of topological cyclic homology by means of a descent spectral sequence. We carry out the computation for a p-adic local field with F-p-coefficients, including the case p = 2 which was only covered by motivic methods except in the totally unramified case.
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作者：Okounkov, A.; Smirnov, A.
作者单位：Columbia University; HSE University (National Research University Higher School of Economics); University of North Carolina; University of North Carolina Chapel Hill; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences
摘要：For an arbitrary Nakajima quiver variety X, we construct an analog of the quantum dynamical Weyl group acting in its equivariant K-theory. The correct generalization of the Weyl group here is the fundamental groupoid of a certain periodic locally finite hyperplane arrangement in Pic(X) circle times C. We identify the lattice part of this groupoid with the operators of quantum difference equation for X. The cases of quivers of finite and affine type are illustrated by explicit examples.
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作者：Buterus, P.; Goetze, F.; Hille, T.; Margulis, G.
作者单位：University of Gottingen; University of Bielefeld; Northwestern University; Yale University
摘要：The number of lattice points in d-dimensional hyperbolic or elliptic shells {m : a < Q[m] < b}, which are restricted to rescaled and growing domains r Omega, is approximated by the volume. An effective error bound of order o(r(d-2)) for this approximation is proved based on Diophantine approximation properties of the quadratic form Q. These results allow to show effective variants of previous non-effective results in the quantitative Oppenheim problem and extend known effective results in dime...
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作者：Berti, Massimiliano; Maspero, Alberto; Ventura, Paolo
作者单位：International School for Advanced Studies (SISSA)
摘要：Small-amplitude, traveling, space periodic solutions -called Stokes waves- of the 2 dimensional gravity water waves equations in deep water are linearly unstable with respect to long-wave perturbations, as predicted by Benjamin and Feir in 1967. We completely describe the behavior of the four eigenvalues close to zero of the linearized equations at the Stokes wave, as the Floquet exponent is turned on. We prove in particular the conjecture that a pair of non-purely imaginary eigenvalues depict...
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作者：De Rosa, Antonio; Tione, Riccardo
作者单位：University System of Maryland; University of Maryland College Park; Max Planck Society
摘要：We prove that m-dimensional Lipschitz graphs with anisotropic mean curvature bounded in L-p, p > m, are regular almost everywhere in every dimension and codimension. This provides partial or full answers to multiple open questions arising in the literature. The anisotropic energy is required to satisfy a novel ellipticity condition, which holds for instance in a C-1,C-1 neighborhood of the area functional. This condition is proved to imply the atomic condition. In particular we provide the fir...
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作者：Kehle, Christoph
作者单位：University of Cambridge; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：The purpose of this paper is to show an unexpected connection between Diophantine approximation and the behavior of waves on black hole interiors with negative cosmological constant Lambda < 0 and explore the consequences of this for the Strong Cosmic Censorship conjecture in general relativity. We study linear scalar perturbations psi of Kerr-AdS solving square(g)psi - 2/3 Lambda psi = 0 with reflecting boundary conditions imposed at infinity. Understanding the behavior of psi at the Cauchy h...
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作者：Merlo, Andrea
作者单位：Universite Paris Saclay
摘要：This paper is devoted to the study of tangential properties of measures with density in the Heisenberg groups H-n. Among other results we prove that measures with (2n + 1)-density have only flat tangents and conclude the classification of uniform measures in H-1.
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作者：Gross, Mark; Siebert, Bernd
作者单位：University of Cambridge; University of Texas System; University of Texas Austin
摘要：As announced in Gross and Siebert (in Algebraic geometry: Salt Lake City 2015, Proceedings of Symposia in Pure Mathematics, vol 97, no 2. AMS, Providence, pp 199-230, 2018) in 2016, we construct and prove consistency of the canonical wall structure. This construction starts with a log Calabi-Yau pair (X, D) and produces a wall structure, as defined in Gross et al. (Mem. Amer. Math. Soc. 278(1376), 1376, 1-103, 2022). Roughly put, the canonical wall structure is a data structure which encodes a...
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作者：Krannich, Manuel
作者单位：University of Cambridge
摘要：We construct a zig-zag from the once delooped space of pseudoiso-topies of a closed 2n-disc to the once looped algebraic K -theory space of the integers and show that the maps involved are p-locally (2n - 4)-connected for n > 3 and large primes p. The proof uses the computation of the stable homology of the moduli space of high-dimensional handlebodies due to Botvinnik-Perlmutter and is independent of the classical approach to pseudoisotopy theory based on Igusa's stability theorem and work of...
