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Seminars

AS-NCTS Geometry Seminar

Analysis, Geometry and Topology of Dirac operators on stratified pseudomanifolds

2024/11/06 (Wed.) 11:00~12:00
  • Date : 2024/11/06 (Wed.) 11:00~12:00
  • Location : Seminar Room 638, Institute of Mathematics (NTU Campus)
  • Speaker : Paolo Piazza (Sapienza Università di Roma)
  • Organizer : Jih-Hsin Cheng (AS) and Siye Wu (National Tsing Hua University)
  • 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.
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