Topology of Algebraic Varieties

University Of Illinois At Chicago, Chicago IL

Investigators

Abstract

DMS-010 Anatoly S. Libgober Concrete issues proposed in this project are the study of 2-variable elliptic genus and chiral deRham complex for non-singular and singular varieties, mathematical foundations of the second quantized elliptic genus and orbifold elliptic genus, ODE and PDE appearing in mirror symmetry, the Chern classes of mirrors and the topology of the complements as well as the study of the fundamental groups of the complements. The goal of this project is to analyze from mathematical point of view several methods and techniques which were used in theoretical physics, more precisely in string theory. Such mathematical investigation should lead to new results in the physical theories involved and produce a broader understanding of the reasons of effectiveness of the methods used by physicists. Particular problems which we are planning to solve are motivated by dualities in string theory and more specifically by mirror correspondence. One of the problems is to find new properties of mirror correspondence and its characterization. This involved the study in topology, algebraic geometry and differential equations.