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作者：Brown, Aaron; Hertz, Federico Rodriguez; Wang, Zhiren
摘要：In this article we prove global rigidity results for hyperbolic actions of higher-rank lattices. Suppose Gamma is a lattice in a semisimple Lie group, all of whose factors have rank 2 or higher. Let a be alpha smooth Gamma-action on a compact nilmanifold M that lifts to an action on the universal cover. If the linear data rho of alpha contains a hyperbolic element, then there is a continuous semiconjugacy intertwining the actions of alpha and rho on a finite-index subgroup of Gamma. If alpha i...
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作者：Abert, Miklos; Bergeron, Nicolas; Biringer, Ian; Gelander, Tsachik; Nikolov, Nikolay; Raimbault, Jean; Samet, Iddo
摘要：We study the asymptotic behaviour of Betti numbers, twisted torsion and other spectral invariants of sequences of locally symmetric spaces. Our main results are uniform versions of the DeGeorge-Wallach Theorem, of a theorem of Delorme and various other limit multiplicity theorems. A basic idea is to adapt the notion of Benjamini-Schramm convergence (BS-convergence), originally introduced for sequences of finite graphs of bounded degree, to sequences of Riemannian manifolds, and analyze the pos...
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作者：Cohn, Henry; Kumar, Abhinav; Miller, Stephen D.; Radchenko, Danylo; Viazovska, Maryna
摘要：Building on Viazovska's recent solution of the sphere packing problem in eight dimensions, we prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing. In particular, we find an optimal auxiliary function for the linear programming bounds, which is an analogue of Viazovska's function for the eight-dimensional case.
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作者：Benoist, Yves; Hulin, Dominique
摘要：We prove that a quasi-isometric map between rank one symmetric spaces is within bounded distance from a unique harmonic map. Inparticular, this completes the proof of the Schoen-Li-Wang conjecture.
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作者：Caraiani, Ana; Scholze, Peter
摘要：The goal of this paper is to show that the cohomology of compact unitary Shimura varieties is concentrated in the middle degree and torsion-free, after localizing at a maximal ideal of the Hecke algebra satisfying a suitable genericity assumption. Along the way, we establish various foundational results on the geometry of the Hodge-Tate period map. In particular, we compare the fibres of the Hodge-Tate period map with Igusa varieties.
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作者：Zhang, Weiping
摘要：We generalize classical theorems due to Lichnerowicz and Hitchin on the existence of Riemannian metrics of positive scalar curvature on spin manifolds to the case of foliated spin manifolds. As a consequence, we show that there is no foliation of positive leafwise scalar curvature on any torus, which generalizes the famous theorem of Schoen-Yau and Gromov-Lawson on the nonexistence of metrics of positive scalar curvature on torus to the case of foliations. Moreover, our method, which is partly...
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作者：Bushnell, Colin J.; Henniart, Guy
摘要：Let F be a non-Archimedean locally compact field. We show that the local Langlands correspondence over F has a strong property generalizing the higher ramification theorem of local class field theory. If pi is an irreducible cuspidal representation of a general linear group GL(n)(F) and sigma the corresponding irreducible representation of the Weil group W-F of F, the restriction of sigma to a ramification subgroup of W-F is determined by a truncation of the simple character theta(pi) containe...
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作者：Moreira, Joel
摘要：An old question in Ramsey theory asks whether any finite coloring of the natural numbers admits a monochromatic pair {x + y, xy}. We answer this question affirmatively in a strong sense by exhibiting a large new class of nonlinear patterns that can be found in a single cell of any finite partition of N. Our proof involves a correspondence principle that transfers the problem into the language of topological dynamics. As a corollary of our main theorem we obtain partition regularity for new typ...
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作者：Yun, Zhiwei; Zhang, Wei
摘要：We define the Heegner Drinfeld cycle on the moduli stack of Drinfeld Shtukas of rank two with r-modifications for an even integer r. We prove an identity between (1) the r-th central derivative of the quadratic base change L-function associated to an everywhere unramified cuspidal automorphic representation pi of PGL(2), and (2) the self-intersection number of the pi-isotypic component of the Heegner Drinfeld cycle. This identity can be viewed as a function-field analog of the Waldspurger and ...
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作者：Viazovska, Maryna S.
摘要：In this paper we prove that no packing of unit balls in Euclidean space R-8 has density greater than that of the E8-lattice packing.
