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作者：Glauberman, George; Lynd, Justin
作者单位：University of Chicago; University of Montana System; University of Montana
摘要：A. Chermak has recently proved that to each saturated fusion system over a finite p-group, there is a unique associated centric linking system. B. Oliver extended Chermak's proof by showing that all the higher cohomological obstruction groups relevant to unique existence of centric linking systems vanish. Both proofs indirectly assume the classification of finite simple groups. We show how to remove this assumption, thereby giving a classification-free proof of the Martino-Priddy conjecture co...
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作者：Inou, Hiroyuki; Mukherjee, Sabyasachi
作者单位：Kyoto University; Constructor University; State University of New York (SUNY) System; Stony Brook University
摘要：It is well known that every rational parameter ray of the Mandelbrot set lands at a single parameter. We study the rational parameter rays of the multicorn , the connectedness locus of unicritical antiholomorphic polynomials of degree d, and give a complete description of their accumulation properties. One of the principal results is that the parameter rays accumulating on the boundaries of odd period (except period 1) hyperbolic components of the multicorns do not land, but accumulate on arcs...
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作者：Abe, Takuro
作者单位：Kyoto University
摘要：Let be the triple of hyperplane arrangements. We show that the freeness of and the division of by imply the freeness of . This division theorem improves the famous addition-deletion theorem, and it has several applications, which include a definition of divisionally free arrangements. It is a strictly larger class of free arrangements than the classical important class of inductively free arrangements. Also, whether an arrangement is divisionally free or not is determined by the combinatorics....
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作者：Bonahon, Francis; Wong, Helen
作者单位：University of Southern California; Carleton College
摘要：We study finite-dimensional representations of the Kauffman bracket skein algebra of a surface S. In particular, we construct invariants of such irreducible representations when the underlying parameter is a root of unity. The main one of these invariants is a point in the character variety consisting of group homomorphisms from the fundamental group to , or in a twisted version of this character variety. The proof relies on certain miraculous cancellations that occur for the quantum trace hom...
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作者：Berman, Robert J.
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：It is shown that any, possibly singular, Fano variety X admitting a Kahler-Einstein metric is K-polystable, thus confirming one direction of the Yau-Tian-Donaldson conjecture in the setting of Q-Fano varieties equipped with their anti-canonical polarization. The proof is based on a new formula expressing the Donaldson-Futaki invariants in terms of the slope of the Ding functional along a geodesic ray in the space of all bounded positively curved metrics on the anti-canonical line bundle of X. ...
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作者：Koberda, Thomas; Santharoubane, Ramanujan
作者单位：University of Virginia; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
摘要：We prove that for each sufficiently complicated orientable surface S, there exists an infinite image linear representation of such that if is freely homotopic to a simple closed curve on S, then has finite order. Furthermore, we prove that given a sufficiently complicated orientable surface S, there exists a regular finite cover such that is not generated by lifts of simple closed curves on S, and we give a lower bound estimate on the index of the subgroup generated by lifts of simple closed c...
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作者：Fraser, Ailana; Schoen, Richard
作者单位：University of British Columbia; Stanford University; University of California System; University of California Irvine
摘要：We prove existence and regularity of metrics on a surface with boundary which maximize sigma(1) L where sigma(1) is the first nonzero Steklov eigenvalue and L the boundary length. We show that such metrics arise as the induced metrics on free boundary minimal surfaces in the unit ball B-n for some n. In the case of the annulus we prove that the unique solution to this problem is the induced metric on the critical catenoid, the unique free boundary surface of revolution in B-3. We also show tha...
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作者：Tiozzo, Giulio
作者单位：Yale University
摘要：The core entropy of polynomials, recently introduced by W. Thurston, is a dynamical invariant which can be defined purely in combinatorial terms, and provides a useful tool to study parameter spaces of polynomials. The theory of core entropy extends the entropy theory for real unimodal maps to complex polynomials: the real segment is replaced by an invariant tree, known as the Hubbard tree, which lies inside the filled Julia set. We prove that the core entropy of quadratic polynomials varies c...
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作者：Anantharaman, Nalini; Leautaud, Matthieu; Macia, Fabricio
作者单位：Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidad Politecnica de Madrid
摘要：We analyse the structure of semiclassical and microlocal Wigner measures for solutions to the linear Schrodinger equation on the disk, with Dirichlet boundary conditions. Our approach links the propagation of singularities beyond geometric optics with the completely integrable nature of the billiard in the disk. We prove a structure theorem, expressing the restriction of the Wigner measures on each invariant torus in terms of second-microlocal measures. They are obtained by performing a finer ...
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作者：Angel, Omer; Hutchcroft, Tom; Nachmias, Asaf; Ray, Gourab
作者单位：University of British Columbia; Tel Aviv University; University of Cambridge
摘要：We show that the circle packing type of a unimodular random plane triangulation is parabolic if and only if the expected degree of the root is six, if and only if the triangulation is amenable in the sense of Aldous and Lyons [1]. As a part of this, we obtain an alternative proof of the Benjamini-Schramm Recurrence Theorem [19]. Secondly, in the hyperbolic case, we prove that the random walk almost surely converges to a point in the unit circle, that the law of this limiting point has full sup...
