Title： Localization of eta invariants

Speaker：Bo Liu  （华东师范大学）

Time：2018年11月23日（周五）    下午 16:00-17:30

Room：东区管理科研楼   数学科学学院1418室

Abstract：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 and Segal 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.