Introduction to Index Theory£¨5 Lectures£©

Hang Wang Íõº½

*(ECNU)*

13:00-14:15, Oct 1-5, 2018 Science Building A510

__Abstract:__

I will talk about the K-theoretic index index theory of an elliptic operator on a manifold invariant under the action of a group (as appeared in the setting of the Baum-Connes assembly map) and some concrete ways of getting cohomological formulas by taking traces on the index in K-theory. These formulas are generalizations of the Atiyah-Singer index formula and are motivations for constructing topological invariants for the space and for its group of symmetries.
Outline:
1. Fredholm index in K-theory, Dirac operators and heat kernel method;
2. L^2-index theorems (and applications) by Atiyah and by Connes-Moscovici;
3. K-theoretic index for equivariant elliptic operators, example of Connes-Kasparov¡¯s isomorphism, relation to L^2-index;
4. Pairing of K-theoretic index with a trace associated to a conjugacy class of the group, applications.

__About the speaker:__

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