报告摘要：The famous Atiyah-Singer index theorem announced in 1963 computed the index of elliptic operators, which is defined analytically, in a topological way, by using the characteristic classes. In 1968, Atiyah andSegal established a localization formula for the equivariant index which computes the equivariant index via the contribution of the fixed point sets of the group action. It is natural to ask if the localization property holds for the more complex spectral invariants, which are not computable in a local way and not a topological invariant.In this talk, we will establish a version of localization formula for equivariant eta-invariants，which were introduced in the 1970's as the boundary contribution of index theorem for compact manifolds with boundary and are formally equal to the number of positive eigenvalues of the Dirac operator minus the number of its negative eigenvalues, by using differential K-theory, a new research field in this century. This is a joint work with Xiaonan Ma.

报告人简介：刘博，华东师范大学数学科学学院青年研究员，紫江青年学者。师从著名几何学家张伟平院士，于2013年毕业于南开大学陈省身数学研究所，获得理学博士学位。于2014.1-2016.12期间，先后在德国科隆大学与德国柏林洪堡大学做博士后工作。主要研究方向为流形上的整体分析，Atiyah-Singer 指标理论，微分K理论。其研究成果发表在国际著名期刊Invent Math、Trans.Amer. Math. Soc.、C. R. Acad. Sci. Paris等。