# Student Working Seminar in Groups and Dynamics

## Fall 2017

 Date: October 4, 2017 Time: 1:00pm Location: BLOC 624 Speaker: Konrad Wróbel Title: Shannon's Entropy I Abstract: I'll begin working through Shannon's classical paper on Entropy and information theory. Date: October 11, 2017 Time: 1:00pm Location: BLOC 628 Speaker: Mehrzad Monzavi/Konrad Wrobel Title: Shannon's Entropy II Abstract: We will finish talking about basic properties of entropy and discuss concentration bounds, the equipartition property and if time permits, the Shannon's Fundamental Theorem for a Noiseless Channel. Date: October 18, 2017 Time: 1:00pm Location: BLOC 628 Speaker: Mehrzad Monzavi Title: Shannon's Entropy III Abstract: I will talk about conditional Shannon entropy, conditional typicality and with time's permission, conditional asymptotic equipartition property. Date: October 25, 2017 Time: 1:00pm Location: BLOC 628 Speaker: Roman Kogan Title: Finite-state automata and measures Abstract: The idea of self-similarity has been prominently used in group theory ever since the introduction of the Grigorchuk group, generated by states of a finite-state machine with output, to answer Milnor's question on intermediate growth of groups. Similar ideas can be applied to the study of measures on the space of sequences in a finite alphabet to define finite-state measures. These measures generalize Bernoulli, Markov and k-step Markov measures in a natural way, and are preserved by the action of invertible finite-state automorphisms. We introduce and briefly discuss the properties of these measures, such as when they are k-step Markov, and when their image under non-invertible automorphisms is finite-state. Date: November 1, 2017 Time: 1:00pm Location: BLOC 628 Speaker: Krzysztof Święcicki Title: Are L^p and l^p coarse equivalent? Abstract: I'll give brief overview of isomorphism problem of L^p and l^p in different categories and cover importance of this question in corse setting. Then I'll prove that there's no equivariant corse embedding of L^p into l^p. Date: November 8, 2017 Time: 1:00pm Location: BLOC 628 Speaker: Justin Cantu Title: Fragmentations and Periodicity of Tree-like Groups Abstract: We introduce the notion of a tree-like action of a group generated by homeomorphisms of the Cantor set with period 2. Under some conditions, we can produce an orbit-equivalent action by a infinite finitely generated periodic group. Date: November 15, 2017 Time: 1:00pm Location: BLOC 628 Speaker: Krzysztof Święcicki Title: Are L^p and l^p coarse equivalent? II Abstract: This time I'll prove why there's no equivariant coarse embedding of L^p into l^p and mention how this can be useful for attacking the general problem of coarse equivalence between the two spaces.