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# Operator Algebra and Noncommutative Geometry Seminar Series

## March 15, 2018 @ 3:30 pm - 4:30 pm

##### Speaker

Associate Professor Adam Rennie (University of Wollongong)

##### Title

The non-unital version of Connes’ theorem on the Hochschild class of the Chern character.

##### Abstract

The theorem in the title captures an analogue of the integral of top degree differential forms on a manifold.

I will describe in a bit more detail what the theorem is about and discuss some of the difficulties and history of extending it to spectral triples over nonunital algebras. Then I will sketch a short proof.

The proof is simple due to its reliance on a refined version of the local index formula, and the consequent understanding of the passage from generalised residues of zeta functions to representations in terms of singular traces. Joint work with Alan Carey.