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作者：Atobe, Hiraku; Gan, Wee Teck
作者单位：University of Tokyo; National University of Singapore
摘要：In this paper, we give an explicit determination of the theta lifting for symplectic-orthogonal and unitary dual pairs over a nonarchimedean field F of characteristic 0. We determine when theta lifts of tempered representations are nonzero, and determine the theta lifts in terms of the local Langlands correspondence.
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作者：Song, Jian; Tian, Gang
作者单位：Rutgers University System; Rutgers University New Brunswick; Peking University; Princeton University
摘要：We prove the existence and uniqueness of the weak Kahler-Ricci flow on projective varieties with log terminal singularities. We also show that the weak Kahler-Ricci flow can be uniquely continued through divisorial contractions and flips if they exist. Finally we propose an analytic version of the minimal model program with Ricci flow.
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作者：Heckman, Gert; Zhao, Lei
作者单位：Radboud University Nijmegen; Nankai University
摘要：Chenciner and Jim,nez-P,rez (Mosc Math J 13(4):621-630, 2013) showed that the range of the spectra of the angular momenta of all the rigid motions of a fixed central configuration in a general Euclidean space form a convex polytope. In this note we explain how this result follows from a general convexity theorem of O'Shea and Sjamaar in real moment map geometry (Math Ann 31:415-457, 2000). Finally, we provide a representation-theoretic description of the pushforward of the normalized measure u...
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作者：Kollar, Janos; Xu, Chenyang
作者单位：Princeton University
摘要：A log Calabi-Yau pair consists of a proper variety X and a divisor D on it such that is numerically trivial. A folklore conjecture predicts that the dual complex of D is homeomorphic to the quotient of a sphere by a finite group. The main result of the paper shows that the fundamental group of the dual complex of D is a quotient of the fundamental group of the smooth locus of X, hence its pro-finite completion is finite. This leads to a positive answer in dimension 4. We also study the dual co...
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作者：Eckhardt, Jonathan; Kostenko, Aleksey
作者单位：Cardiff University; University of Vienna
摘要：Motivated by the study of certain nonlinear wave equations (in particular, the Camassa-Holm equation), we introduce a new class of generalized indefinite strings associated with differential equations of the form -u = z u omega + z(2) u nu on an interval [0, L), where is a real-valued distribution in H-loc(-1), nu is a non-negative Borel measure on [0, L) and z is a complex spectral parameter. Apart from developing basic spectral theory for these kinds of spectral problems, our main result is ...
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作者：Deraux, Martin; Parker, John R.; Paupert, Julien
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Durham University; Arizona State University; Arizona State University-Tempe
摘要：We produce a family of new, non-arithmetic lattices in PU(2, 1). All previously known examples were commensurable with lattices constructed by Picard, Mostow, and Deligne-Mostow, and fell into nine commensurability classes. Our groups produce five new distinct commensurability classes. Most of the techniques are completely general, and provide efficient geometric and computational tools for constructing fundamental domains for discrete groups acting on the complex hyperbolic plane.
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作者：Gan, Wee Teck; Ichino, Atsushi
作者单位：National University of Singapore; Kyoto University
摘要：We establish the Fourier-Jacobi case of the local Gross-Prasad conjecture for unitary groups, by using local theta correspondence to relate the Fourier-Jacobi case with the Bessel case established by Beuzart-Plessis. To achieve this, we prove two conjectures of Prasad on the precise description of the local theta correspondence for (almost) equal rank unitary dual pairs in terms of the local Langlands correspondence. The proof uses Arthur's multiplicity formula and thus is one of the first exa...
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作者：Berger, Pierre
作者单位：Universite Paris 13
摘要：We show, for every or , the existence of a Baire generic set of -families of -maps of a manifold M of dimension 2, so that for every a small the map has infinitely many sinks. When the dimension of the manifold is 3, the generic set is formed by families of diffeomorphisms. When M is the annulus, this generic set is formed by local diffeomorphisms. This is a counter example to a conjecture of Pugh and Shub.
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作者：Biquard, Olivier
作者单位：Sorbonne Universite; Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We calculate a wall crossing formula for 4-dimensional Poincare-Einstein metrics, through a wall made of orbifold Poincare-Einstein metrics with singularities. This is based on a formalism which enables to deal with higher order terms of the Einstein equation in this setting. Some other consequences are deduced.
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作者：Braverman, Alexander; Kazhdan, David; Patnaik, Manish M.
作者单位：Brown University; Hebrew University of Jerusalem; University of Alberta
摘要：This paper is a continuation of Braverman and Kazhdan (Ann Math (2) 174(3):1603-1642, 2011) in which the first two authors have introduced the spherical Hecke algebra and the Satake isomorphism for an untwisted affine Kac-Moody group over a non-archimedian local field. In this paper we develop the theory of the Iwahori-Hecke algebra associated to these same groups. The resulting algebra is shown to be closely related to Cherednik's double affine Hecke algebra. Furthermore, using these results,...
