Inventiones mathematicae

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• Depth functions of symbolic powers of homogeneous ideals AI翻译
  作者：Hop Dang Nguyen; Ngo Viet Trung
  作者单位：Vietnam Academy of Science & Technology (VAST); Vietnam Academy of Science & Technology (VAST)
  摘要：This paper addresses the problem of comparing minimal free resolutions of symbolic powers of an ideal. Our investigation is focused on the behavior of the function depthR/I(t)=dimR-pdI(t)-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\,\mathrm{depth}\,}}R/I{(t)} = \dim R -{{\,\mathrm{pd}\,}}I{(t)} - 1$$\end{do...
• An optimal uncertainty principle in twelve dimensions via modular forms AI翻译
  作者：Cohn, Henry; Goncalves, Felipe
  作者单位：Microsoft; University of Alberta; University of Bonn
  摘要：We prove an optimal bound in twelve dimensions for the uncertainty principle of Bourgain, Clozel, and Kahane. Suppose f : R-12 -> R is an integrable function that is not identically zero. Normalize its Fourier transform (f) over cap by (f) over cap(xi) = integral(Rd) f(x)e(-2 pi i < x,xi >) dx, and suppose (f) over cap is real-valued and integrable. We show that if f (0) <= 0, (f) over cap (0) <= 0, f (x) = 0 for vertical bar x vertical bar >= r(1), and (f) over cap(xi) = 0 for vertical bar xi...
• Surjective word maps and Burnside's theorem AI翻译
  作者：Guralnick, Robert M.; Liebeck, Martin W.; O'Brien, E. A.; Shalev, Aner; Tiep, Pham Huu
  作者单位：University of Southern California; Imperial College London; University of Auckland; Hebrew University of Jerusalem; Rutgers University System; Rutgers University New Brunswick
  摘要：We prove surjectivity of certain word maps on finite non-abelian simple groups. More precisely, we prove the following: if N is a product of two prime powers, then the word map is surjective on every finite non-abelian simple group; if N is an odd integer, then the word map is surjective on every finite quasisimple group. These generalize classical theorems of Burnside and Feit-Thompson. We also prove asymptotic results about the surjectivity of the word map that depend on the number of prime ...
• Global bifurcations in the two-sphere: a new perspective AI翻译
  作者：Ilyashenko, Yu.; Kudryashov, Yu.; Schurov, I.
  作者单位：HSE University (National Research University Higher School of Economics); Cornell University
  摘要：We construct an open set of structurally unstable three parameter families whose weak and so called moderate topological classification defined below has a numerical invariant that may take an arbitrary positive value. Here and below families are families of vector fields in the two-sphere. This result disproves an Arnold's conjecture of 1985. Then we construct an open set of six parameter families whose moderate topological classification has a functional invariant. This invariant is an arbit...
• Polyharmonic capacity and Wiener test of higher order AI翻译
  作者：Mayboroda, Svitlana; Maz'ya, Vladimir
  作者单位：University of Minnesota System; University of Minnesota Twin Cities; Linkoping University; Peoples Friendship University of Russia
  摘要：In the present paper we establish the Wiener test for boundary regularity of the solutions to the polyharmonic operator. We introduce a new notion of polyharmonic capacity and demonstrate necessary and sufficient conditions on the capacity of the domain responsible for the regularity of a polyharmonic function near a boundary point. In the case of the Laplacian the test for regularity of a boundary point is the celebrated Wiener criterion of 1924. It was extended to the biharmonic case in dime...
• Unique ergodicity for foliations in P2 with an invariant curve AI翻译
  作者：Dinh, Tien-Cuong; Sibony, Nessim
  作者单位：National University of Singapore; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
  摘要：Consider a foliation in the projective plane admitting a projective line as the unique invariant algebraic curve. Assume that the foliation is generic in the sense that its singular points are hyperbolic. We show that there is a unique positive dd(c)-closed (1, 1)-current of mass 1 which is directed by the foliation and this is the current of integration on the invariant line. A unique ergodicity theorem for the distribution of leaves follows: for any leaf L, appropriate averages of L converge...
• Two-bubble dynamics for threshold solutions to the wave maps equation AI翻译
  作者：Jendrej, Jacek; Lawrie, Andrew
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris 13; Massachusetts Institute of Technology (MIT)
  摘要：We consider the energy-critical wave maps equation in the equivariant case, with equivariance degree . It is known that initial data of energy and topological degree zero leads to global solutions that scatter in both time directions. We consider the threshold case of energy . We prove that the solution is defined for all time and either scatters in both time directions, or converges to a superposition of two harmonic maps in one time direction and scatters in the other time direction. In the ...
• Global rigid inner forms and multiplicities of discrete automorphic representations AI翻译
  作者：Kaletha, Tasho
  摘要：We study the cohomology of certain Galois gerbes over number fields. This cohomology provides a bridge between refined local endoscopy, as introduced in Kaletha (Ann Math (2) 184(2):559-632, 2016), and classical global endoscopy. As particular applications, we express the canonical adelic transfer factor that governs the stabilization of the Arthur-Selberg trace formula as a product of normalized local transfer factors, we give an explicit constriction of the pairing between an adelic L-packet...
• On the nature of the generating series of walks in the quarter plane AI翻译
  作者：Dreyfus, Thomas; Hardouin, Charlotte; Roques, Julien; Singer, Michael F.
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); North Carolina State University
  摘要：In the present paper, we introduce a new approach, relying on the Galois theory of difference equations, to study the nature of the generating series of walks in the quarter plane. Using this approach, we are not only able to recover many of the recent results about these series, but also to go beyond them. For instance, we give for the first time hypertranscendency results, i.e., we prove that certain of these generating series do not satisfy any nontrivial nonlinear algebraic differential eq...
• Canonical bases arising from quantum symmetric pairs AI翻译
  作者：Bao, Huanchen; Wang, Weiqiang
  作者单位：University System of Maryland; University of Maryland College Park; University of Virginia
  摘要：We develop a general theory of canonical bases for quantum symmetric pairs with parameters of arbitrary finite type. We construct new canonical bases for the finite-dimensional simple -modules and their tensor products regarded as -modules. We also construct a canonical basis for the modified form of the quantum group . To that end, we establish several new structural results on quantum symmetric pairs, such as bilinear forms, braid group actions, integral forms, Levi subalgebras (of real rank...