Derived categories in string theory

Date: Aug. 1, 3, 5, 8, 10, 12,   14:00--15:30

Venue:Conference Hall 213, Science Building

Title: Derived categories in string theory

Speaker: Eric Sharpe, Assistant Professor of Physics

                  Virginia Polytechnic Institute and State University

Abstract:In recent years, categories have come to play an important role in mathematical string theory.  In these lectures, I shall describe one particular example in detail. Specifically, I will describe how derived categories of coherent sheaves appear in physics, as an efficient description of systems of D-branes, anti-D-branes, and tachyons in the open string B model topological field theory. After a short introduction outlining general features of categories in physics, I will work through properties of the closed and open string B model, showing how derived categories arise physically and outlining various applications to e.g. correlation function computations, notions of stability, and defects in CFT. As time permits, I will then discuss B-twisted Landau-Ginzburg models in closed and open strings, matrix factorizations, and the role of derived categories in such theories.