题目： Regularized Integrals on Riemann Surfaces and Modular Forms

报告人：李 思，清华大学

时间：2022年7月27日 （星期三）下午 4:00-5:00

地点：东区管理科研楼1418教室

摘要：We introduce a simple procedure to integrate differential forms with arbitrary holomorphic poles on Riemann surfaces. It gives rise to an intrinsic regularization of such singular integrals in terms of the underlying conformal geometry.  This regularization scheme establishes an analytic theory for integrals over configuration spaces, including correlation functions arising from two dimensional chiral quantum field theories.  As an application, we show regularized integrals on elliptic curves provide geometric modular completions of quasi-modular forms of the corresponding A-cycle integrals. This is joint work with Jie Zhou.