主讲人：韩飞 教授（新加坡国立大学） 

时  间： 10月31日（周一）15：30-16：30

地  点：数学科学学院 311 教室

备  注：Abstract: Witten genus is the loop space analogue of the Hirzebruch A-hat genus. On a string manifold, the Witten genus is a modular form and is the equivariant index  of the Dirac operator on the free loop space. The homotopy refinement of the Witten genus leads to the theory of topological modular forms. Hohn and Stolz also conjectured that existence of a positive Ricci curvature metric on a string manifold implies the vanishing of the Witten genus. In this talk, I will discuss two extensions of the classical Witten genus. One concerns a generalization of string manifolds, which we call string^c manifolds and the other one is the mod 2 extension. We will present vanishing results for these generalized Witten genera on complete intersections and describe a possible mod 2 extension of the Hohn-Stolz conjecture. The talk is based on the joint work with Qingtao Chen and Weiping Zhang.