Eta invariant and analytic torsion

開催日時
2016/04/12 火 16:45 - 18:15
場所
6号館609号室
講演者
Xianzhe Dai
講演者所属
University of California
概要

Eta invariant and analytic torsion are the two prominent spectral invariants arising from index theory. The eta invariant is the boundary contribution to the index formula and measures the spectral asymmetry. The analytic torsion, on the other hand, is a certain combination of determinants of Laplacians, and gives analytic interpretation of the Reidemeister torsion, a topological invariant which is not homotopy invariant (and hence is very useful in finer classifications). Each has higher dimensional generalizations and noncommutative geometric extensions. In this talk, I will review these developments and discuss our work with Weiping Zhang on the relation between these two invariants.