-
作者：Marmi, Stefano; Moussa, Pierre; Yoccoz, Jean-Christophe
摘要：A standard interval exchange map is a one-to-one map of the interval which is locally a translation except at finitely many singularities. We define for such maps, in terms of the Rauzy-Veech continuous fraction algorithm, a diophantine arithmetical condition called restricted Roth type which is almost surely satisfied in parameter space. Let T-0 be a standard interval exchange map of restricted Roth type, and let r be an integer >= 2. We prove that, amongst Cr+3 deformations of T-0 which are ...
-
作者：Pellarin, Federico
摘要：We introduce a class of deformations of the values of the Goss zeta function. We prove, with the use of the theory of deformations of vectorial modular forms as well as with other techniques, a formula for their value at 1, and some arithmetic properties of values at other positive integers. Our formulas involve Anderson and Thakur's function omega. We discuss how our formulas may be used to investigate the existence of a kind of functional equation for the Gosszeta function.
-
作者：Brock, Jeffrey F.; Canary, Richard D.; Minsky, Yair N.
摘要：Thurston's Ending Lamination Conjecture states that a hyperbolic 3-manifold N with finitely generated fundamental group is uniquely determined by its topological type and its end invariants. In this paper we prove this conjecture for Kleinian surface groups; the general case when N has incompressible ends relative to its cusps follows readily. The main ingredient is a uniformly bilipschitz model for the quotient of H-3 by a Kleinian surface group.
-
作者：Burns, K.; Masur, H.; Wilkinson, A.
摘要：We prove that the geodesic flow for the Weil-Petersson metric on the moduli space of Riemann surfaces is ergodic (and in fact Bernoulli) and has finite, positive metric entropy.
-
作者：Barak, Boaz; Rao, Anup; Shaltiel, Ronen; Wigderson, Avi
摘要：The main result of this paper is an explicit disperser for two independent sources on n bits, each of min-entropy k = 2(log beta n), where beta < 1 is some absolute constant. Put differently, setting N = 2(n) and K = 2(k), we construct an explicit N x N Boolean matrix for which no K x K sub-matrix is monochromatic. Viewed as the adjacency matrix of a bipartite graph, this gives an explicit construction of a bipartite K-Ramsey graph of 2N vertices. This improves the previous bound of k = o(n) o...
-
作者：Dieulefait, Luis
摘要：Let F be a totally real Galois number field. We prove the existence of base change relative to the extension F/Q for every holomorphic newform of weight at least 2 and odd level, under simple local assumptions on the field F.
-
作者：Marques, Fernando Coda
摘要：In this paper we prove that the moduli space of metrics with positive scalar curvature of an orientable compact three-manifold is path-connected. The proof uses the Ricci flow with surgery, the conformal method, and the connected sum construction of Gromov and Lawson. The work of Perelman on Hamilton's Ricci flow is fundamental. As one of the applications we prove the path-connectedness of the space of trace-free asymptotically flat solutions to the vacuum Einstein constraint equations on R-3.
-
作者：Brown, Francis
摘要：We prove that the category of mixed Tate motives over Z is spanned by the motivic fundamental group of P-1 minus three points. We prove a conjecture by M. Hoffman which states that every multiple zeta value is a Q-linear combination of zeta(n(1), . . . ,n(r)), where n(i) is an element of {2,3}.
-
作者：Green, Ben; Tao, Terence
摘要：A theorem of Leibman asserts that a polynomial orbit (g(n)Gamma)(n is an element of Z) on a nilmanifold G/Gamma is always equidistributed in a union of closed sub-nilmanifolds of G/Gamma. In this paper we give a quantitative version of Leibman's result, describing the uniform distribution properties of a finite polynomial orbit (g(n)Gamma)(n is an element of[N]) in a nilmanifold. More specifically we show that there is a factorisation g = epsilon g'gamma, where epsilon(n) is smooth, (gamma(n)G...
-
作者：Marshall, Simon
摘要：We prove a power saving for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on GL(2) over any number field that is not totally real. Our proof involves the theory of p-adically completed cohomology developed by Calegari and Emerton and a bound for the growth of coinvariants in certain finitely generated noncommutative Iwasawa modules.
