Mathematics Department

Operator Algebras and Dynamics Seminar

Fall 2016

All talks are from 3:45-4:45 p.m. in the Seminar room, unless otherwise specified.

  • Aug
    26
  • Character Rigidity for Lattices in Lie Groups
    Darren Creutz
    USNA
    Location: CH320
    Time: 03:45 PM

    View Abstract

    Characters on groups (positive definite conjugation-invariant functions) arise naturally both from probability-preserving actions (the measure of the set of fixed points) and unitary representations on finite factors (the trace); the classical theory of characters is the first step in the classification of finite simple groups and culminates in the Peter-Weyl theorem for compact groups. I will present the results of J. Peterson and myself that the only characters on lattices in semisimple groups are the left-regular character and the classical characters. This is in actuality operator-algebraic superrigidity for lattices, answering a question of Connes. The main idea is to bring dynamics into the operator-algebraic picture; the second half of the talk will focus on the ergodic-theoretic ideas of contractiveness and the Poisson boundary and how these ideas lead to operator-algebraic results.
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