MATHEMATICS SEMINAR by Dulip Piyaratne Author:COLLEGE OF SCIENCESTime: 14:30Location: SCI 103
Algebraic varieties are the geometric objects given as the zero sets of polynomials. Classical algebraic geometry studies varieties directly. But a more modern approach is to study the varieties indirectly via some algebraic objects associated to them. In particular, the theory of derived categories provides an efficient algebraic platform to investigate the hidden geometric information of a variety. They also have emerged as important objects in string theory.
Sheaf-theoretic models of D-branes can be interpreted as objects in derived categories. Motivated by Douglas’s work on Pi-stability for D-branes, Bridgeland introduced the notion of stability conditions in the categorical setup. His approach can be considered as an abstraction of the usual slope stability for sheaves. In this talk, I will explain how to construct such stability conditions on the derived categories of some Calabi-Yau threefolds, and their applications to study Donaldson-Thomas invariants and derived equivalences. These are the joint works with A. Maciocia, G. Oberdieck, and Y. Toda. |