A tracial characterization of Furstenberg's x p, x q conjecture

Abstract: Furstenberg's conjecture about xp, xq, invariant measures on $[0,1)$, where p and q are multiplicatively independent integers, is one of the most fundamental open problems in ergodic theory. We will see how the topological counterpart of this conjecture, which is a theorem due to Furstenberg, implies the uniqueness of the $C^*$-norm on the complex group ring of a certain metabelian group $G$.

Furthermore, we will present a characterization of the xp,xq conjecture in terms of the traces of $C^*(G)$, and discuss the primitive ideal space and K-theory of $C^*(G)$. This is based on joint work with Chris Bruce.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | slides | video )

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Noncommutative geometry in NYC

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