Room 617, Institute of Mathematics, Academia Sinica

(中研院數學所 617室)

Analysis, Geometry and Topology of Dirac operators on stratified pseudomanifolds

Paolo Piazza (Sapienza Università di Roma)

**Abstract**

I will present results about Dirac operators on stratified pseudomanifolds.I will concentrate mainly on the signature operator on an orientable stratified pseudomanifolds, for example a singular projective variety, but I will also touch briefly the case of the spin-Dirac operator on a spin-pseudomanifold. I will first focus on giving a survey of the main theorems concerning the Fredholm index, and more generally the K-homology class, associated to a Dirac operator satisfying the so-called Witt assumption, with particular emphasis on the two examples I have already mentioned. I will then move to recent results in collaboration with Pierre Albin and Markus Banagl. I will explain how to define, analytically, wrong-way maps in K-homology in this stratified context and how they are related to existing wrong-way maps in topology. I will then end my talk by illustrating a fundamental property of these wrong-way maps, namely that they preserve the signature K-homology class.

**Organizers：**Jih-Hsin Cheng (AS), Siye Wu (NTHU)