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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 ...
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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...
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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...
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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...
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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 ...
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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...
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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...
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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...
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作者：Kleinbock, D. Y.; Margulis, G. A.
作者单位：Brandeis University; Yale University
摘要：One of the propositions in the paper (Kleinbock and Margulis in Invent Math 138(3):451-494, 1999), related to approximating certain sets by smooth functions, was recently found to be incorrect. Here, we correct the mistake.
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作者：McGerty, Kevin; Nevins, Thomas
作者单位：University of Oxford; University of Illinois System; University of Illinois Urbana-Champaign
摘要：For algebraic varieties defined by hyperkahler or, more generally, algebraic symplectic reduction, it is a long-standing question whether the hyperkahler Kirwan map on cohomology is surjective. We resolve this question in the affirmative for Nakajima quiver varieties. We also establish similar results for other cohomology theories and for the derived category. Our proofs use only classical topological and geometric arguments.
