Inventiones mathematicae

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• The topological structure of scaling limits of large planar maps AI翻译
  作者：Le Gall, Jean-Francois
  作者单位：Universite PSL; Ecole Normale Superieure (ENS)
  摘要：We discuss scaling limits of large bipartite planar maps. If p >= 2 is a fixed integer, we consider, for every integer n >= 2, a random planar map M (n) which is uniformly distributed over the set of all rooted 2p-angulations with n faces. Then, at least along a suitable subsequence, the metric space consisting of the set of vertices of M-n , equipped with the graph distance rescaled by the factor n(-1/4), converges in distribution as n -> infinity towards a limiting random compact metric spac...
• Dimension of the Torelli group for Out(Fn) AI翻译
  作者：Bestvina, Mladen; Bux, Kai-Uwe; Margalit, Dan
  作者单位：Utah System of Higher Education; University of Utah; University of Virginia
  摘要：Let T-n be the kernel of the natural map Out( F-n). GL(n)( Z). We use combinatorial Morse theory to prove that Tn has an Eilenberg-MacLane space which is ( 2n - 4)- dimensional and that H2n-4( T-n, Z) is not finitely generated ( n >= 3). In particular, this shows that the cohomological dimension of Tn is equal to 2n-4 and recovers the result of Krstic-McCool that T-3 is not finitely presented. We also give a new proof of the fact, due to Magnus, that T-n is finitely generated.
• Derivation of the cubic non-linear Schrodinger equation from quantum dynamics of many-body systems AI翻译
  作者：Erdos, Laszlo; Schlein, Benjamin; Yau, Horng-Tzer
  作者单位：University of Munich; Harvard University
  摘要：We prove rigorously that the one-particle density matrix of three dimensional interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of the cubic non-linear Schrodinger equation in a suitable scaling limit. The result is extended to k-particle density matrices for all positive integer k.
• Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces AI翻译
  作者：Mirzakhani, Maryam
  作者单位：Princeton University
• Transcendence measures and algebraic growth of entire functions AI翻译
  作者：Coman, Dan; Poletsky, Evgeny A.
  作者单位：Syracuse University
  摘要：In this paper we obtain estimates for certain transcendence measures of an entire function f. Using these estimates, we prove Bernstein, doubling and Markov inequalities for a polynomial P(z,w) in C-2 along the graph of f. These inequalities provide, in turn, estimates for the number of zeros of the function P(z,f(z)) in the disk of radius r, in terms of the degree of P and of r. Our estimates hold for arbitrary entire functions f of finite order, and for a subsequence {n (j) } of degrees of p...
• Embedding of hyperbolic groups into products of binary trees AI翻译
  作者：Buyalo, Sergei; Dranishnikov, Alexander; Schroeder, Viktor
  作者单位：Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences; State University System of Florida; University of Florida; University of Zurich
  摘要：We show that every Gromov hyperbolic group Gamma admits a quasi-isometric embedding into the product of n+1 binary trees, where n=dim partial derivative(infinity) Gamma is the topological dimension of the boundary at infinity of Gamma.
• The homotopy theory of dg-categories and derived Morita theory AI翻译
  作者：Toen, Bertrand
  作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
  摘要：The main purpose of this work is to study the homotopy theory of dg-categories up to quasi-equivalences. Our main result is a description of the mapping spaces between two dg-categories C and D in terms of the nerve of a certain category of (C,D)-bimodules. We also prove that the homotopy category Ho(dg-Cat) possesses internal Hom's relative to the (derived) tensor product of dg-categories. We use these two results in order to prove a derived version of Morita theory, describing the morphisms ...
• Complex zeros of real ergodic eigenfunctions AI翻译
  作者：Zelditch, Steve
  作者单位：Johns Hopkins University
  摘要：We determine the limit distribution (as lambda -> infinity) of complex zeros for holomorphic continuations p(lambda)(C) to Grauert tubes of real eigenfunctions of the Laplacian on a real analytic compact Riemannian manifold (M, g) with ergodic geodesic flow. If {p(jk)} is an ergodic sequence of eigenfunctions, we prove the weak limit formula 1/lambda j [Z(pjk)(C)] -> i/pi partial derivative partial derivative vertical bar xi vertical bar(g), where [Z(pjk)(C)] is the current of integration over...
• The Kodaira dimension of the moduli of K3 surfaces AI翻译
  作者：Gritsenko, V. A.; Hulek, K.; Sankaran, G. K.
  作者单位：Universite de Lille; Leibniz University Hannover; University of Bath
  摘要：The global Torelli theorem for projective K3 surfaces was first proved by Piatetskii-Shapiro and Shafarevich 35 years ago, opening the way to treating moduli problems for K3 surfaces. The moduli space of polarised K3 surfaces of degree 2d is a quasi-projective variety of dimension 19. For general d very little has been known hitherto about the Kodaira dimension of these varieties. In this paper we present an almost complete solution to this problem. Our main result says that this moduli space ...
• Right-veering diffeomorphisms of compact surfaces with boundary AI翻译
  作者：Honda, Ko; Kazez, William H.; Matic, Gordana
  作者单位：University of Southern California; University System of Georgia; University of Georgia
  摘要：We initiate the study of the monoid of right-veering diffeomorphisms on a compact oriented surface with nonempty boundary. The monoid strictly contains the monoid of products of positive Dehn twists. We explain the relationship to tight contact structures and open book decompositions.