Lecture Series on Operator Algebras and Index Theory (Lecture 1)

Ryszard Nest

*(University of Copenhagen)*

16:00-17:30, Oct 15, 2020 Zoom 467 658 1686

__Abstract:__

Here is the list of topics for the whole lecture series (6 lectures in total, every Thursday, same time).
I will not necessarily keep the order and some of it will sketchy, but will hopefully touch upon all of them.
0.1. Fredholm Index.
0.2. Basic example: Shubin calculus and the case of Rn (Bott periodicity).
0.3. K-theory, K-homology and index pairing.
0.4. Kasparov product, (decorated) KK-category, assembly map, Baum-Connes, Kaplansky, Novikov, ... conjectures.
0.5. Geometric examples, MacKean-Singer formula and its variants,
heat kernel expansion and the tangential groupoid.
0.6. von Neumann algebra valued index.
0.7. Cyclic homology, cohomology and index.
0.8. Symbol calculi, algebraic index theorems and applications.
0.9. Connes-Moscovici local index formulas.
0.10. Fourier integral operators, group actions and more examples
of index computations.

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