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作者：Bader, Uri; Fisher, David; Miller, Nicholas; Stover, Matthew
摘要：Let Gamma be a lattice in SO0(n, 1). We prove that if the associated locally symmetric space contains infinitely many maximal totally geodesic subspaces of dimension at least 2, then Gamma is arithmetic. This answers a question of Reid for hyperbolic n-manifolds and, independently, McMullen for hyperbolic 3-manifolds. We prove these results by proving a superrigidity theorem for certain representations of such lattices. The proof of our superrigidity theorem uses results on equidistribution fr...
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作者：Zhang, W.
摘要：We study a partially linearized version of the relative trace formula for the arithmetic Gan-Gross-Prasad conjecture for the unitary group U(V). The linear factor in this relative trace formula provides an SL2-symmetry which allows us to prove by induction the arithmetic fundamental lemma over Q(p) when p is odd and p >= dim V.
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作者：Birkar, Caucher
摘要：We study log canonical thresholds (also called global log canonical threshold or alpha-invariant) of R-linear systems. We prove existence of positive lower bounds in different settings, in particular, proving a conjecture of Ambro. We then show that the Borisov-Alexeev-Borisov conjecture holds; that is, given a natural number d and a positive real number epsilon, the set of Fano varieties of dimension d with epsilon-log canonical singularities forms a bounded family. This implies that biration...
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作者：Harvey, David; van der Hoeven, Joris
摘要：We present an algorithm that computes the product of two n-bit integers in O (n log n) bit operations, thus confirming a conjecture of Schonhage and Strassen from 1971. Our complexity analysis takes place in the multitape Turing machine model, with integers encoded in the usual binary representation. Central to the new algorithm is a novel Gaussian resampling technique that enables us to reduce the integer multiplication problem to a collection of multidimensional discrete Fourier transforms o...
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作者：Beuzart-Plessis, Raphael; Liu, Yifeng; Zhang, Wei; Zhu, Xinwen
摘要：We introduce a new technique for isolating components on the spectral side of the trace formula. By applying it to the Jacquet-Rallis relative trace formula, we complete the proof of the global Gan-Gross-Prasad conjecture and its refinement Ichino-Ikeda conjecture for U(n) x U(n + 1) in the stable case.
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作者：Oh, Sung-Jin; Tataru, Daniel
摘要：This article represents the fourth and final part of a four-paper sequence whose aim is to prove the Threshold Conjecture as well as the more general Dichotomy Theorem for the energy critical 4 + 1-dimensional hyperbolic Yang Mills equation. The Threshold Theorem asserts that topologically trivial solutions with energy below twice the ground state energy are global and scatter. The Dichotomy Theorem applies to solutions in arbitrary topological class with large energy, and provides two exclusi...
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作者：Dang, Nguyen-Bac; Favre, Charles
摘要：We prove that dynamical degrees of rational self-maps on projective varieties can be interpreted as spectral radii of naturally defined operators on suitable Banach spaces. Generalizing Shokurov's notion of b-divisors, we consider the space of b-classes of higher codimension cycles, and endow this space with various Banach norms. Building on these constructions, we design a natural extension to higher dimensions of the Picard-Manin space introduced by Cantat and Boucksom-Favre-Jonsson in the c...
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作者：Dac, Tuan Ngo
摘要：We study Todd-Thakur's analogues of Zagier-Hoffman's conjectures in positive characteristic. These conjectures predict the dimension and an explicit basis J(w) of the span of characteristic p multiple zeta values of fixed weight w which were introduced by Thakur as analogues of classical multiple zeta values of Euler. In the present paper we first establish the algebraic part of these conjectures which states that the span of characteristic p multiple zeta values of weight w is generated by th...
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作者：Stefanov, Plamen; Uhlmann, Gunther; Vasy, Andras
摘要：In this paper we analyze the local and global boundary rigidity problem for general Riemannian manifolds with boundary (M,g). We show that the boundary distance function, i.e., d(g)vertical bar(x)(partial derivative M)(partial derivative M), known near a point p is an element of partial derivative M at which partial derivative M is strictly convex, determines g in a suitable neighborhood of p in M, up to the natural diffeomorphism invariance of the problem. We also consider the closely related...
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作者：Chang, Huai-Liang; Guo, Shuai; Li, Jun
摘要：We prove two structure theorems for the Gromov-Witten theory of the quintic threefolds, which together give an effective algorithm for the all genus Gromov-Witten potential functions of quintics. By using these structure theorems, we prove Yamaguchi-Yau's Polynomial Ring Conjecture in this paper and prove Bershadsky-Cecotti-Ooguri-Vafa's Feynman rule conjecture in the subsequent paper.
