Analysis Seminar

Unless specified, all seminars are
Wednesday 4-5pm at 250 Math Building.

April
10th
**Xin Ma**, Texas A&M University

Paradoxical comparison and pure infiniteness of
reduced crossed product C*-algebras

*Abstract*: In this talk, I will talk about the relation
between comparison phenomenon in topological dynamical systems and
pure infiniteness of the reduced crossed products. In particular, we
will see that dynamical comparison implies pure infiniteness of
reduced crossed product under the assumption that there is no
invariant ergodic probability Borel measures. In addition, for an
action which is not necessarily minimal, I will introduce a new
notion called paradoxical comparison, which is a generalization of
dynamical comparison in the case that there is no invariant ergodic
probability Borel measures. We will see that paradoxical comparison
also implies the pure infiniteness of the reduced crossed product if
there are only finitely many invariant closed subsets of the action.
If time permits, I will talk about more applications of paradoxical
comparison.

April
17th
**Felipe García-Ramos**, Universidad Autonoma de San Luis
Potosi

Topological
hierarchy of dynamical systems with discrete spectrum

*Abstract*: Dynamical systems with discrete spectrum (via the
Koopman L^2 operator) are simple systems from a measure theoretic
perspective. Nonetheless, from a topological point of view they can
exhibit a range of behaviors. Several recent results have built a
hierarchy to understand the topological complexity of these systems.

April
24th
**Sebastián Barbieri**, University of British Columbia

How
to find aperiodic subshifts on countable groups

*Abstract*: We will show that for any countable group G there
is a non-empty, G-invariant and closed subset X of {0,1}^G on which
G acts freely by translations. This was first proven by Gao, Jackson
and Seward using an intricate construction. We shall present a "one
page proof" which is based on a probabilistic tool: the Lovász local
lemma. This is joint work with Nathalie Aubrun and Stéphan Thomassé.

Past Analysis Seminar
_{ }