ON-LINE - Operator algebras seminar

Speaker: Philipp Schmitt (University of Copenhagen)

Title: The local algebraic index theorem.

Abstract: The Atiyah-Singer index theorem has an important algebraic analogue in the context of deformation quantizations, the algebraic index theorem. This theorem relates the trace on a deformed algebra with an integral of certain characteristic classes, and can be used to obtain obstructions for the existence of strict deformations.

In this talk, I will introduce formal deformation quantizations, in order to discuss the algebraic index theorem and its local version. I will obtain explicit formulas for the algebraic trace density, that allow to prove the index theorem in a more elementary way, and that can possibly be used to construct secondary invariants in the future.

This is ongoing and joint work with Alexander Gorokhovsky and Ryszard Nest.


Zoom link: https://ucph-ku.zoom.us/j/68821510821