Operator Algebras and Dynamics Seminar
Spring 2019
All talks are from 3:454:45 p.m. in the Seminar room, unless otherwise specified.

Apr16

Jing ZhouUniversity of MarylandTime: 03:45 PM

Apr01

Group actions on product systems and KtheoryValentin DeaconuU. NevadaRenoTime: 03:45 PM
View Abstract
Product systems $Y$ over various semigroups were introduced by N. Fowler, inspired by work of W. Arveson. We will recall the definition of $Y$ and introduce group actions and crossed products $Y\rtimes G$. One motivation is group actions on higher rank graphs. We generalize a result of C. Schafhauser for a rowfinite and faithful product system $Y$ indexed by ${\mathbb N}^k$ concerning the $K$theory of the crossed product by the gauge action $\gamma$. The main result is $K_*({\mathcal O}_A(Y)\rtimes_\gamma{\mathbb T}^k)\cong \varinjlim_{n \in {\mathbb N}^k} (K_*(A),[Y_n]), where $[Y_n]$ denotes the homomorphism induced by $Y_n$ via Fredholm operators. We apply this result to a product system constructed from group representations.

Mar25

Ergodicity on Fractal Spaces via Hyperbolic GeometryAnton LukyanenkoGeorge Mason UniversityTime: 03:45 PM
View Abstract
Continued fractions on the real numbers have farreaching applications, including connections to dynamics, Diophantine approximation, and hyperbolic geometry. Their generalizations, both in R and in higher dimensions have been a topic of extensive study over the last few decades. A central question has been the extent to which all points have the same CFbased properties, i.e. whether the associated Gauss map is ergodic. I will discuss an approach used by Hensley, based on the use of transfer operators, to argue that the Gauss map for complex continued fractions is ergodic; with connections to the work of Mauldin, Urbanski, and others. Then, I will describe the recent generalization of the theory to a more general class of spaces, where instead one can use hyperbolic geometry to prove ergodicity, extending the classical approach of Artin and Series.

Feb25

Mixing properties for infinite local complexity tiling substitutionsRobbie RobinsonGeorge Washington UniversityTime: 03:45 PM
View Abstract
Discrete substitution and finite local complexity substitution tiling dynamical systems can be weakly mixing but not strongly mixing. We discuss examples of infinite local complexity substitution tilings (in d=1 and d=2) that are mixing of all orders and have Lebesgue spectrum. We compare to results on other types of dynamical systems including interval exchanges and rank 1.

Jan28

Local weak∗Convergence, algebraic actions, and a maxmin principleBen HayesUniversity of VirginiaTime: 03:45 PM
View Abstract
This talk will be concerned with algebraic actions, which are actions of a countable, discrete, group G on a compact group X. When G is sofic, a natural question is when the topological entropy and measure entropy of these actions agree. I will show that there is a complete lattice of "generalized subgroups" of X and a maxmin principle in this complete lattice which essentially gives a complete answer to when this equality occurs.