Abstract:
Dirac operators have played a crucial role in linking different branches of mathematics and physics. As differential operators, they established a bridge between topology and geometry, and are essential ingredients of gauge theories, including the Standard Model of particle physics. In this talk, I will first give a short review of the basic properties of Dirac operators, with an emphasis on index theorems. Then I will talk about their relationship with supersymmetric quantum field theory, where the supercharge plays the role of Dirac operator and the corresponding index is known as elliptic genus. For two dimensional supersymmetric gauge theories, the elliptic genera can be computed by Jeffrey-Kirwan residues through the localization technique. I will give an introduction to this method along with some of its applications.
Biography:
Jirui Guo is a Postdoctoral Researcher at Fudan University. He received his bachelor's and master's degrees in mathematics from East China Normal University and Ph.D. degree in physics from Virginia Polytechnic Institute and State University. His research interests are in string theory and supersymmetric quantum field theories.