作者：Chelkak, Dmitry; Smirnov, Stanislav
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; St. Petersburg Scientific Centre of the Russian Academy of Sciences; Saint Petersburg State University; University of Geneva
摘要：It is widely believed that the celebrated 2D Ising model at criticality has a universal and conformally invariant scaling limit, which is used in deriving many of its properties. However, no mathematical proof has ever been given, and even physics arguments support (a priori weaker) Mobius invariance. We introduce discrete holomorphic fermions for the 2D Ising model at criticality on a large family of planar graphs. We show that on bounded domains with appropriate boundary conditions, those ha...
作者：Pop, Florian
作者单位：University of Pennsylvania
摘要：Recall that a program initiated by Bogomolov in 1990 aims at reconstructing function fields K vertical bar k with td(K vertical bar k) > 1 and k algebraically closed from the maximal pro-l abelian-by-central Galois group Pi(c)(K) of K, where l is any prime number not equal char(k). In this paper we complete that program in the case k is an algebraic closure of a finite field.
作者：Teleman, Constantin
摘要：I classify the cohomological 2D field theories based on a semi-simple complex Frobenius algebra A. They are controlled by a linear combination of kappa-classes and by an extension datum to the Deligne-Mumford boundary. Their effect on the Gromov-Witten potential is described by Givental's Fock space formulae. This leads to the reconstruction of Gromov-Witten (ancestor) invariants from the quantum cup-product at a single semi-simple point and the first Chern class of the manifold, confirming Gi...
