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作者：Bader, Uri; Furman, Alex; Sauer, Roman
作者单位：Technion Israel Institute of Technology; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; University of Chicago
摘要：We study rigidity properties of lattices in , na parts per thousand yen3, and of surface groups in in the context of integrable measure equivalence. The results for lattices in , na parts per thousand yen3, are generalizations of Mostow rigidity; they include a cocycle version of strong rigidity and an integrable measure equivalence classification. Despite the lack of Mostow rigidity for n=2 we show that cocompact lattices in allow a similar integrable measure equivalence classification.
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作者：Hida, Haruzo
作者单位：University of California System; University of California Los Angeles
摘要：Let pa parts per thousand yen5 be a prime. If an irreducible component of the spectrum of the 'big' ordinary Hecke algebra does not have complex multiplication, under mild assumptions, we prove that the image of its mod p Galois representation contains an open subgroup of for the canonical weight variable T. This fact appears to be deep, as it is almost equivalent to the vanishing of the mu-invariant of the Kubota-Leopoldt p-adic L-function and the anticyclotomic Katz p-adic L-function. Anothe...
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作者：Scholze, Peter
作者单位：University of Bonn
摘要：We show how the Langlands-Kottwitz method can be used to determine the semisimple local factors of the Hasse-Weil zeta-function of certain Shimura varieties. This is made possible by a new result describing part of the nearby cycle sheaves in certain situations. In combination with a general base-change lemma in harmonic analysis, we use this to prove a conjecture of Haines and Kottwitz for these Shimura varieties.
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作者：Blocki, Zbigniew
作者单位：Jagiellonian University
摘要：We prove a conjecture of N. Suita which says that for any bounded domain D in a, one has , where c (D) (z) is the logarithmic capacity of a,a-D with respect to zaD and K (D) the Bergman kernel on the diagonal. We also obtain optimal constant in the Ohsawa-Takegoshi extension theorem.
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作者：Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther
作者单位：University of Cambridge; University of Jyvaskyla; University of Washington; University of Washington Seattle; University of California System; University of California Irvine
摘要：We show that on simple surfaces the geodesic ray transform acting on solenoidal symmetric tensor fields of arbitrary order is injective. This solves a long standing inverse problem in the two-dimensional case.
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作者：Pappas, G.; Zhu, X.
作者单位：Michigan State University; Northwestern University
摘要：We give a group theoretic definition of local models as sought after in the theory of Shimura varieties. These are projective schemes over the integers of a p-adic local field that are expected to model the singularities of integral models of Shimura varieties with parahoric level structure. Our local models are certain mixed characteristic degenerations of Grassmannian varieties; they are obtained by extending constructions of Beilinson, Drinfeld, Gaitsgory and the second-named author to mixe...
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作者：Alper, Jarod; Fedorchuk, Maksym; Smyth, David Ishii
作者单位：Universidad de los Andes (Colombia); Columbia University; Harvard University
摘要：We prove that a generic canonically or bicanonically embedded smooth curve has semistable mth Hilbert points for all ma parts per thousand yen2. We also prove that a generic bicanonically embedded smooth curve has stable mth Hilbert points for all ma parts per thousand yen3. In the canonical case, this is accomplished by proving finite Hilbert semistability of special singular curves with -action, namely the canonically embedded balanced ribbon and the canonically embedded balanced double A (2...
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作者：Merle, Frank; Raphael, Pierre; Rodnianski, Igor
作者单位：CY Cergy Paris Universite; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Princeton University
摘要：We consider the energy critical Schrodinger map problem with the 2-sphere target for equivariant initial data of homotopy index k=1. We show the existence of a codimension one set of smooth well localized initial data arbitrarily close to the ground state harmonic map in the energy critical norm, which generates finite time blowup solutions. We give a sharp description of the corresponding singularity formation which occurs by concentration of a universal bubble of energy.
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作者：Mischler, Stephane; Mouhot, Clement
作者单位：Universite PSL; Universite Paris-Dauphine; University of Cambridge
摘要：This paper is devoted to the study of propagation of chaos and mean-field limits for systems of indistinguishable particles, undergoing collision processes. The prime examples we will consider are the many-particle jump processes of Kac and McKean (Kac in Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954-1955, Vol. III, pp. 171-197, 1956; McKean in J. Comb. Theory 2:358-382, 1967) giving rise to the Boltzmann equation. We solve the conjecture raised b...
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作者：Lackenby, Marc; Meyerhoff, Robert
作者单位：University of Oxford; Boston College
