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• The Smale conjecture and min-max theory AI翻译
  作者：Ketover, Daniel; Liokumovich, Yevgeny
  作者单位：Rutgers University System; Rutgers University New Brunswick; University of Toronto; University Toronto Mississauga
  摘要：We give a new proof of the Smale conjecture for RP3 and all lens spaces using minimal surfaces and min-max theory. For RP3, the conjecture was first proved in 2019 by Bamler-Kleiner using Ricci flow.
• Solvability of the Lp Dirichlet problem for the heat equation is equivalent to parabolic uniform rectifiability in the case of a parabolic Lipschitz graph AI翻译
  作者：Bortz, Simon; Hofmann, Steve; Martell, Jose Maria; Nystrom, Kaj
  作者单位：University of Alabama System; University of Alabama Tuscaloosa; University of Missouri System; University of Missouri Columbia; Universidad Carlos III de Madrid; Complutense University of Madrid; Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM); CSIC - Instituto de Ciencias Matematicas (ICMAT); Autonomous University of Madrid; Uppsala University
  摘要：We prove that if a parabolic Lipschitz (i.e., Lip(1,1/2)) graph domain has the property that its caloric measure is a parabolic A(infinity) weight with respect to surface measure (which in turn is equivalent to L(p )solvability of the Dirichlet problem for some finite p), then the function defining the graph has a half-order time derivative in the space of (parabolic) bounded mean oscillation. Equivalently, we prove that the A(infinity) property of caloric measure implies, in this case, that t...
• Quillen stratification in equivariant homotopy theory AI翻译
  作者：Barthel, Tobias; Castellana, Natalia; Heard, Drew; Naumann, Niko; Pol, Luca
  作者单位：Max Planck Society; Autonomous University of Barcelona; Centre de Recerca Matematica (CRM); Norwegian University of Science & Technology (NTNU); University of Regensburg
  摘要：We prove a version of Quillen's stratification theorem in equivariant homotopy theory for a finite group G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$G$\end{document}, generalizing the classical theorem in two directions. Firstly, we work with arbitrary commutative equivariant ring spectra as coefficients, and s...
• The 27 geodesic networks in the directed landscape AI翻译
  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...
• Compatibility of canonical l-adic local systems on adjoint Shimura varieties AI翻译
  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...
• Counting pseudo-Anosovs as weakly contracting isometries AI翻译
  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...
• The metamathematics of separated determinacy AI翻译
  作者：Aguilera, J. P.
  作者单位：Technische Universitat Wien; University of Vienna; Ghent University
  摘要：Determinacy axioms are mathematical principles which assert that various infinite games are determined. In this article, we prove three general meta-theorems on the logical strength of determinacy axioms. These allow us to reduce a metamathematical analysis of the principle of Gamma-determinacy over a weak base theory to an analysis of aprinciple Gamma '-determinacy, where Gamma ' is a strictly smaller complexity class than Gamma.Themeta-theorems are proved in the weak theoryRCA0. However, the...
• Bordifications of the moduli spaces of tropical curves and abelian varieties, and unstable cohomology of SLg(Z) AI翻译
  作者：Brown, Francis
  摘要：We con We construct bordifications of the moduli spaces of tropical curves and of tropical abelian varieties, and show that the tropical Torelli map extends to their bordifications. We prove that the classical bi-invariant differential forms studied by Cartan and others extend to these bordifications by studying their behaviour at infinity, and consequently deduce infinitely many new non-zero unstable classes in the cohomology of the general and special linear groups GL(g)(Z) and SLg(Z). In pa...
• Logarithmic double ramification cycles AI翻译
  作者：Holmes, D.; Molcho, S.; Pandharipande, R.; Pixton, A.; Schmitt, J.
  作者单位：Leiden University; Leiden University - Excl LUMC; Sapienza University Rome; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Michigan System; University of Michigan
  摘要：Let A = (a1,..., an) be a vector of integers which sum to k(2g - 2+ n). The double ramification cycle DRg,A is an element of CHg(Mg,n) on the moduli space of curves is the virtual class of an Abel-Jacobi locus of pointed curves (C, x1,..., xn) satisfying OC(Sigma i=1naixi)similar or equal to(omega Clog)k.. The Abel-Jacobi construction requires log blow-ups of M g,n to resolve the indeterminacies of the Abel-Jacobi map. Holmes (J. Inst. Math. Jussieu 2019) has shown that DRg, A admits a canonic...
• Global solutions for 1D cubic dispersive equations, part III: the quasilinear Schrödinger flow AI翻译
  作者：Ifrim, Mihaela; Tataru, Daniel
  作者单位：University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Berkeley
  摘要：The first target of this article is the local well-posedness question for 1D quasilinear Schr & ouml;dinger equations with cubic nonlinearities. The study of this class of problems, in all dimensions, was initiated in pioneering work of Kenig-Ponce-Vega for localized initial data, and then continued by Marzuola-Metcalfe-Tataru for initial data in Sobolev spaces. Our objective here is to fully redevelop the study of this problem in the 1D case, and to prove a sharp local well-posedness result. ...