报告题目：Modular Forms and Anomaly Cancellation: An Application of Index Theory in Quantum Field Theory and String Theory

报 告 人：韩飞 副教授 （新加坡国立大学）

报告时间：2025年7月8日（星期二） 9:30-10:30

报告地点：数学科学学院114（小报告厅）

校内联系人： 李风玲 教授         联系电话：84708351-8515

报告摘要：Anomalies arise in quantum field theory when classical symmetries fail to persist upon quantization, posing obstructions to defining consistent physical theories. In string theory and M-theory, remarkable formulas have been discovered, such as the Green–Schwarz and Alvarez–Gaumé–Witten anomaly cancellation formulas, ensuring these quantum theories are well defined.

In this talk, I will explain how these anomaly cancellation formulas can be understood and unified using ideas from the theory of modular forms and the Atiyah–Singer index theorem. We will begin with the physics motivation, then discuss the mathematical formulation of anomalies in terms of index theory and characteristic classes, and finally present how modular invariance yields generalized cancellation formulas in various dimensions. Time permitting, I will also describe recent generalizations to M-theory and the role of the Witten genus and modularity in this context.

The talk will be accessible to graduate students with a basic background in differential geometry and topology, and will illustrate beautiful interactions between geometry, topology, number theory, and theoretical physics.

报告人简介：The speaker, HAN Fei, works in the areas of differential geometry, topology, and mathematical physics. He is currently an Associate Professor at the National University of Singapore. His research has been published in renowned journals such as Mathematische Annalen, Advances in Mathematics, Communications in Mathematical Physics, Journal of Differential Geometry, among others. He has been invited to speak at major conferences, including String Math 2023 and the International Congress of Chinese Mathematicians. He currently also serves as an editor for the journal Reviews in Mathematical Physics.