Mathematics Department

Operator Algebras and Dynamics Seminar

Spring 2017

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

  • Feb
    27
  • Trivial Centralizers of High Complexity Toeplitz Systems
    MIDN 1/C James Talisse
    USNA
    Time: 03:45 PM

    View Abstract

    Given a dynamical system $(X,G)$, the centralizer consists of all homeomorphisms of $X$ which commute with the action of the group $G$. In this talk we present a construction of Toeplitz systems over $\mathbb{Z}^d$ which have a trivial centralizer. Historically, trivial centralizers arise from zero entropy systems. However this construction can lead to examples of systems with positive entropy and trivial centralizers.
  • Feb
    13
  • Obstruction to Lifting Cocycles on Groupoids and Associated C*-Algebras
    Marius Ionescu
    USNA
    Time: 03:45 PM
  • Feb
    06
  • The Normal Subgroup Theorem for Lattices in Products (Property (T))
    Darren Creutz
    USNA
    Time: 03:45 PM

    View Abstract

    Margulis' Normal Subgroup Theorem states that if Gamma is an irreducible lattice in a higher-rank semisimple Lie group with trivial center then every nontrivial normal subgroup of Gamma has finite index. Moving away from Lie groups, Bader and Shalom proved that the same result holds for lattices in products of arbitrary simple nondiscrete locally compact groups. I will present joint work with Y. Shalom which gives a new proof of this result and explain how it leads into my work on a conjecture of Margulis and Zimmer about the nature of commensurated subgroups of lattices. The proof is in two distinct halves (as was Margulis'): we prove Gamma / N is finite by showing it is both amenable and has Kazhdan's property (T). The first discussed the amenability proof; this talk will present the (T) half. In particular, this talk will be a standalone talk and will not assume knowledge of what was talked about in part one.
  • Jan
    23
  • The Normal Subgroup Theorem for Lattices in Products (Part One -- Amenability)
    Darren Creutz
    USNA
    Time: 03:45 PM

    View Abstract

    Margulis' Normal Subgroup Theorem states that if Gamma is an irreducible lattice in a higher-rank semisimple Lie group with trivial center then every nontrivial normal subgroup of Gamma has finite index. Moving away from Lie groups, Bader and Shalom proved that the same result holds for lattices in products of arbitrary simple nondiscrete locally compact groups. I will present joint work with Y. Shalom which gives a new proof of this result and explain how it leads to my work with J. Peterson that every ergodic action of an irreducible lattice in a product of higher-rank semisimple groups on a nonatomic probability space is essentially free. The proof is in two distinct halves (as was Margulis'): we prove Gamma / N is finite by showing it is both amenable and has Kazhdan's property (T). Part one will discuss the amenability proof; part two (to be scheduled) will discuss (T). Note: part two will not rely on part one; each talk will be stand-alone.
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