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作者：Grushevsky, Samuel; Hulek, Klaus
作者单位：Leibniz University Hannover; State University of New York (SUNY) System; Stony Brook University
摘要：We study the locus of intermediate Jacobians of cubic threefolds within the moduli space of complex principally polarized abelian fivefolds, and its generalization to arbitrary genus-the locus of abelian varieties with a singular odd two-torsion point on the theta divisor. Assuming that this locus has expected codimension g (which we show to be true for ga parts per thousand currency sign5, and conjecturally for any g), we compute the class of this locus, and of its closure in the perfect cone...
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作者：Lemou, Mohammed; Mehats, Florian; Raphael, Pierre
作者单位：Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); Universite de Rennes; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We consider the three dimensional gravitational Vlasov Poisson system which is a canonical model in astrophysics to describe the dynamics of galactic clusters. A well known conjecture (Binney, Tremaine in Galactic Dynamics, Princeton University Press, Princeton, 1987) is the stability of spherical models which are nonincreasing radially symmetric steady states solutions. This conjecture was proved at the linear level by several authors in the continuation of the breakthrough work by Antonov (S...
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作者：Cadoret, Anna; Tamagawa, Akio
作者单位：Kyoto University; Centre National de la Recherche Scientifique (CNRS); Inria; Universite de Bordeaux
摘要：Let k be a field finitely generated over Q and p a prime. The torsion conjecture (resp. p-primary torsion conjecture) for abelian varieties over k predicts that the k-rational torsion (resp. the p-primary k-rational torsion) of a d-dimensional abelian variety A over k should be bounded only in terms of k and d. These conjectures are only known for d = 1. The p-primary case was proved by Y. Manin, in 1969; the general case was completed by L. Merel, in 1996, after a series of contributions by B...
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作者：Zhang, Wei
作者单位：Harvard University
摘要：We present a relative trace formula approach to the Gross-Zagier formula and its generalization to higher-dimensional unitary Shimura varieties. As a crucial ingredient, we formulate a conjectural arithmetic fundamental lemma for unitary Rapoport-Zink spaces. We prove the conjecture when the Rapoport-Zink space is associated to a unitary group in two or three variables.
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作者：Oh, Hee; Shah, Nimish
作者单位：Brown University; Korea Institute for Advanced Study (KIAS); University System of Ohio; Ohio State University
摘要：Let P be a locally finite circle packing in the plane C invariant under a non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When Gamma is geometrically finite, we construct an explicit Borel measure on C which describes the asymptotic distribution of small circles in P, assuming that either the critical exponent of Gamma is strictly bigger than 1 or P does not contain an infinite bouquet of tangent circles glued at a parabolic fixed point of Gamma. Our construction also ...
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作者：Rolla, Leonardo T.; Sidoravicius, Vladas
作者单位：Universite PSL; Ecole Normale Superieure (ENS)
摘要：We study the long-time behavior of conservative interacting particle systems in Z: the activated random walk model for reaction-diffusion systems and the stochastic sandpile. We prove that both systems undergo an absorbing-state phase transition.
