Isoradial homomorphisms and non-commutative geometry

Devarshi Mukherjee (University of Göttingen)

Thursday 28th January, 2021 16:00-17:00 Contact the organizers for zoom coordinates

Abstract

 

In this talk, I will describe a framework to study smooth subalgebras of algebras arising in non-commutative geometry. More precisely, given a C*-algebra A, we would like to make sense of a "smooth" subalgebra A^∞ ⊆ A, and deduce properties about A using such a subalgebra. Such a smooth subalgebra should be analogous to the Frechet algebra C^∞(M) ⊆ C(M) for a smooth manifold M, in the world of commutative C*-algebras. We shall review the fundamental properties and applications of such embeddings, called isoradial embeddings, due to Ralf Meyer. If time permits, I will mention an ongoing research program with Meyer, Cortiñas and Cuntz, that uses such embeddings to develop non-commutative geometry over finite fields. I will not assume that the audience has any background beyond familiar examples of C*-algebras. A lot of the motivation would however be clearer to those familiar with cyclic homology or operator algebraic K-theory.

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