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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.