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作者：Tang, Moxun
作者单位：Michigan State University
摘要：We give a positive answer to a conjecture of Berestycki and Lions in 1983 on the uniqueness of bound states to Delta u+f(u)=0 in R-n, u is an element of H1(R-n), u not equivalent to 0, n >= 3 . For the model nonlinearity f(u)=-u+|u|(p-1)u1 <(n+2)/(n-2), arising from finding standing waves of Klein-Gordon equation or nonlinear Schrodinger equation, we show that, for each integer k >= 1, the problem has a unique solution u=u(|x|),x is an element of & Ropf;(n), up to translation and reflection, t...
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作者：Arana-Herrera, Francisco; Calderon, Aaron
作者单位：University System of Maryland; University of Maryland College Park; University of Chicago
摘要：Cutting a hyperbolic surface X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$X$\end{document} along a simple closed multi-geodesic results in a hyperbolic structure on the complementary subsurface. We study the distribution of the shapes of these subsurfaces in moduli space as boundary lengths go to infinity, showi...
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作者：Dauvergne, Duncan
作者单位：University of Toronto
摘要：The directed landscape is a random directed metric on the plane that arises as the scaling limit of classical metric models in the KPZ universality class. Typical pairs of points in the directed landscape are connected by a unique geodesic. However, there are exceptional pairs of points connected by more complicated geodesic networks. We show that, up to isomorphism, exactly 27 geodesic networks exist in the directed landscape. We also find Hausdorff dimensions in a scaling-adapted metric on R...
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作者：Chidambaram, Nitin Kumar; Garcia-Failde, Elba; Giacchetto, Alessandro
作者单位：Max Planck Society; University of Edinburgh; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universitat Politecnica de Catalunya; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP); CEA; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We construct and study various properties of a negative spin version of the Witten r-spin class. By taking the top Chern class of a certain vector bundle on the moduli space of spin curves that parametrises r-th roots of the anticanonical bundle, we construct a non-semisimple cohomological field theory (CohFT) that we call the Theta class Theta r. This CohFT does not have a flat unit and its associated Dubrovin-Frobenius manifold is nowhere semisimple. Despite this, we construct a semisimple d...
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作者：Shankar, Arul; Sodergren, Anders; Templier, Nicolas
作者单位：University of Toronto; Chalmers University of Technology; University of Gothenburg; Cornell University
摘要：The Dedekind zeta functions of infinitely many non-Galois cubic fields have negative central values.
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作者：Zubrilina, Nina
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We establish the first case of the surprising correlation phenomenon observed in the recent works of He, Lee, Oliver, Pozdnyakov, and Sutherland between Fourier coefficients in families of modular forms and their root numbers. We give a complete description of the resulting correlation functions for holomorphic modular forms of any fixed weight k and examine the asymptotic properties of these functions.
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作者：Frantzikinakis, Nikos; Kuca, Borys
作者单位：University of Crete; Jagiellonian University
摘要：We give necessary and sufficient conditions for joint ergodicity results of collections of sequences with respect to systems of commuting measure preserving transformations. Combining these results with a new technique that we call seminorm smoothing, we settle several conjectures related to multiple ergodic averages of commuting transformations with polynomial iterates. We show that the Host-Kra factor is characteristic for pairwise independent polynomials, and that under certain ergodicity c...
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作者：Klevdal, Christian; Patrikis, Stefan
作者单位：University of California System; University of California San Diego; University System of Ohio; Ohio State University
摘要：For a Shimura variety (G,X) in the superrigid regime and neat level subgroup K0, we show that the canonical family of l-adic representations associated to a number field point y is an element of ShK0(G,X)(F), {rho y,l:Gal(Q/F)-> Gad(Ql)}l, form a compatible system of Gad(Ql)-representations: there is an integer N(y) such that for all l, rho y,l is unramified away from N(y)l, and for all l not equal l ' and v inverted iota N(y)ll ', the semisimple parts of the conjugacy classes of rho y,l(Frobv...
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作者：Choi, Inhyeok
作者单位：Korea Institute for Advanced Study (KIAS)
摘要：We show that pseudo-Anosov mapping classes are generic in every Cayley graph of the mapping class group of a finite-type hyperbolic surface. Our method also yields an analogous result for rank-one CAT(0) groups and hierarchically hyperbolic groups with Morse elements. Finally, we prove that Morse elements are generic in every Cayley graph of groups that are quasi-isometric to (well-behaved) hierarchically hyperbolic groups. This gives a quasi-isometry invariant theory of counting group element...
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作者：Gomide, Otavio M. L.; Guardia, Marcel; Seara, Tere M.; Zeng, Chongchun
作者单位：Universidade Federal de Goias; University of Barcelona; Centre de Recerca Matematica (CRM); Universitat Politecnica de Catalunya; Universitat Politecnica de Catalunya; University System of Georgia; Georgia Institute of Technology
摘要：Breathers are nontrivial time-periodic and spatially localized solutions of nonlinear dispersive partial differential equations (PDEs). Families of breathers have been found for certain integrable PDEs but are believed to be rare in non-integrable ones such as nonlinear Klein-Gordon equations. In this paper we show that small amplitude breathers of any temporal frequency do not exist for semilinear Klein-Gordon equations with generic analytic odd nonlinearities. A breather with small amplitude...
