In 1995, Bismut and Lott defined a real analytic torsion form as the generalization of the Ray-Singer analytic torsion to the family case. For a smooth fibration with a flat complex vector bundle, they proved a smooth version of the Riemann-Roch-Grothendieck theorem, relating the characteristic classes of the flat bundle on the total space of the fibration to those of its direct image on the base manifold. They also improved the theorem to the level of differential forms, where the torsion forms appear naturally as the transgression forms. In this talk we will give an introduction to the theory of Bismut-Lott torsion forms. We will also talk about our joint work with Martin Puchol and Yeping Zhang.
朱家林，博士毕业于法国巴黎大学（原巴黎七大），先后在南开大学陈省身数学研究所与上海数学中心从事研究工作，现为重庆理工大学数学科学研究中心特聘教授。朱家林教授的主要研究专长为基础数学指标理论中解析挠率与解析挠率形式的研究，在 Anal. PDE, Israel J. Math. 等国际学术期刊发表文章多篇。