Activities This Week

Time reversal symmetry arises in many dynamical systems. In particular, it is an important aspect of dynamical systems which emerge from physical theories such as classical mechanics, thermodynamics and quantum mechanics. In this talk, we introduce the notion of a reversible dynamical system in symbolic dynamics. We investigate conjugacy invariants of a topological Markov chain which possesses an involutory reversing symmetry.

In this talk I will prove that any pseudo-finite group contains an infinite abelian subgroup. Additionally, I shall also discuss some other results concerning pseudo-finite groups and centralizers.

This is joint work with Nadja Hempel.

I will describe the theory of hyperbolic flows on three manifolds, and then describe a new approach to chaotic flows using knot theory, allowing for topological analysis of singular flows. I’ll use this to show that, surprisingly, the famous Lorenz flow on R^3 can be related to the geodesic flow on the modular surface. When changing the parameters, we also find a new type of topological phases in the Lorenz system. This will be an introductory talk.

In this talk I will describe joint work with Chris Phillips and Qingyun Wang. The weak tracial Rokhlin property for actions of discrete amenable groups on simple unital C-algebras is defined by Qingyun Wang [https://arxiv.org/abs/1410.8170]. We show that the class of simple separable unital exact C-algebras with strict comparison and almost divisible Cuntz semigroup is closed under taking crossed products by such actions. We use this to show that the class of simple separable unital nuclear $\mathcal{Z}$-stable C*-algebras is also preserved.

Examples include the non-commutative Bernoulli shift of any discrete amenable group $\Gamma$ on $\bigotimes_{\Gamma} \mathcal{Z} \cong \mathcal{Z}$ and others.