# 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. |