报告题目：Spectral flow and Maslov index: a common computational root

报告人：Prof. Alessandro Portaluri，Università di Torino，Italy

报告时间：2017.3.16 星期四 15:30

报告地点：知新楼B 1032

摘要：Spectral flow is an integer-valued homotopy invariant for paths of selfadjoint Fredholm operators introduced by Atiyah-Patodi and Singer in the seventies in connection with the eta-invariant and the spectral asymmetry. Its finite dimensional counterpart is represented by the Maslov index of a path of Lagrangian subspaces which is generically given by an algebrai count of the intersections of the path with a subvariety called the Maslov cycle. It is well-know that both this invariants are related by the so-called spectral flow formulas which represents the main purposes of the modern index theory.

In this  talk we introduce both this invariants, putting on evidence their common properties and we discuss an efficient method to compute them. If times permits we’ll discuss the theory of partial signatures and how to compute this invariants for analytic paths in some degenerate situation. We close the talk by mention some open problems and new conjecture on this topic.