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KK-theory in geometry and physics

Bram Mesland
Institution: 
Universität Bonn
Location: 
A-134
Schedule: 
Friday, May 4, 2018 - 11:00 to 12:00
Abstract: 

Kasparov's $KK$-theory is a bivariant homology theory for $C^*$-algebras providing a general framework for index theory. Cycles for the theory come from the abstract analogue of a first-order differential operator. After an exposition of the theory for non-specialists, I will discuss some recent results. These include analytic properties of self-adjoint operators, applications of $KK$-theory in the theory of arithmetic manifolds and automorphic forms and the physics of topological insulators.

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