-
作者：Eskin, Alex; Mirzakhani, Maryam; Mohammadi, Amir
摘要：We prove results about orbit closures and equidistribution for the SL(2, R) action on the moduli space of compact Riemann surfaces, which are analogous to the theory of unipotent flows. The proofs of the main theorems rely on the measure classification theorem of the first two authors and a certain isolation property of closed SL(2, R) invariant manifolds developed in this paper.
-
作者：Meeks, William H., III; Perez, Joaquin; Ros, Antonio
摘要：In 1997, Collin proved that any properly embedded minimal surface in R-3 with finite topology and more than one end has finite total Gaussian curvature. Hence, by an earlier result of Lopez and Ros, catenoids are the only nonplanar, nonsimply connected, properly embedded, minimal planar domains in R-3 of finite topology. In 2005, Meeks and Rosenberg proved that the only simply connected, properly embedded minimal surfaces in R-3 are planes and helicoids. Around 1860, Riemann defined a one-para...
-
作者：Bhargava, Manjul; Shankar, Arul
摘要：We prove a theorem giving the asymptotic number of binary quartic forms having bounded invariants; this extends, to the quartic case, the classical results of Gauss and Davenport in the quadratic and cubic cases, respectively. Our techniques are quite general and may be applied to counting integral orbits in other representations of algebraic groups. We use these counting results to prove that the average rank of elliptic curves over Q, when ordered by their heights, is bounded. In particular,...
-
作者：Hough, Bob
摘要：We answer a question of Erdos by showing that the least modulus of a distinct covering system is at most 10(16).
-
作者：Arakawa, Tomoyuki
摘要：We prove the rationality of all the minimal series principal W-algebras discovered by Frenkel, Kac and Wakimoto, thereby giving a new family of rational and C-2-cofinite vertex operator algebras. A key ingredient in our proof is the study of Zhu's algebra of simple W-algebras via the quantized Drinfeld-Sokolov reduction. We show that the functor of taking Zhu's algebra commutes with the reduction functor. Using this general fact we determine the maximal spectrums of the associated graded of Zh...
-
作者：Razborov, Alexander A.
摘要：A pseudorandom generator G(n) : {0, 1}(n) -> {0, 1}(m) is hard for a propositional proof system P if (roughly speaking) P cannot efficiently prove the statement G(n) (x(1),...,x(n)) not equal b for any string b is an element of {0, 1}(m). We present a function (m >= 2(n Omega(1))) generator which is hard for Res(epsilon log n); here Res(k) is the propositional proof system that extends Resolution by allowing k-DNFs instead of clauses. As a direct consequence of this result, we show that whenev...
-
作者：Clozel, Laurent; Thorne, Jack A.
摘要：We apply automorphy lifting techniques to establish new cases of symmetric power functoriality for Hilbert modular forms of regular algebraic weight. The proof is based on a novel application of an automorphy lifting theorem for residually reducible Galois representations.
-
作者：Chelkak, Dmitry; Hongler, Clement; Izyurov, Konstantin
摘要：We rigorously prove the existence and the conformal invariance of scaling limits of the magnetization and multi-point spin correlations in the critical Ising model on arbitrary simply connected planar domains. This solves a number of conjectures coming from the physical and the mathematical literature. The proof relies on convergence results for discrete holomorphic spinor observables and probabilistic techniques.
-
作者：Guan, Qi'an; Zhou, Xiangyu
摘要：In this paper, we prove an L-2 extension theorem with an optimal estimate in a precise way, which implies optimal estimate versions of various well-known L-2 extension theorems. As applications, we give proofs of a conjecture of Suita on the equality condition in Suita's conjecture, the so-called L-conjecture, and the extended Suita conjecture. As other applications, we give affirmative answer to a question by Ohsawa about limiting case for the extension operators between the weighted Bergman ...
-
作者：Lieblich, Max
摘要：Using geometric methods we prove the standard period-index conjecture for the Brauer group of a field of transcendence degree 2 over F-p.
