Talks will be given on zoom, if you have the password you can join here. Please send an email to one of the organizers to get the the password.

If you would like to give a talk, please send the title, abstract and related papers (if available) of your proposed talk to one of the organizers by email.

Organizers: Amir Mohammadi, Anthony Sanchez, Brandon Seward

Winter 2022 Speakers Past Speakers

**January 6:**Gil Goffer (Weizmann Institute of Science)

**Title:**Is invariable generation hereditary?

**Abstract:**We will discuss the notion of invariably generated groups, with various motivating examples. We will then see how hyperbolic groups and small cancellation theory are used in answering the question in the title, which was asked by Wiegold and by Kantor-Lubotzky-Shalev. This is a joint work with Nir Lazarovich.

video

**January 13:**Siyuan Tang (Indiana University)

**Title:**Nontrivial time-changes of unipotent flows on quotients of Lorentz groups

**Abstract:**The theory of unipotent flows plays a central role in homogeneous dynamics. Time-changes are a simple perturbation of a given flow. In this talk, we shall discuss the rigidity of time-changes of unipotent flows. More precisely, we shall see how to utilize the branching theory of the complementary series, combining it with the works of Ratner and Flaminio-Forni to get to our purpose.

video

**January 27:**Sebastián Barbieri Lemp (Universidad de Santiago de Chile)

**Title:**Self-simulable groups

**Abstract:**We say that a finitely generated group is self-simulable if every action of the group on a zero-dimensional space which is effectively closed (this means it can be described by a Turing machine in a specific way) is the topological factor of a subshift of finite type on said group. Even though this seems like a property which is very hard to satisfy, we will show that these groups do exist and that their class is stable under commensurability and quasi-isometries of finitely presented groups. We shall present several examples of well-known groups which are self-simulable, such as Thompson's V and higher-dimensional general linear groups. We shall also show that Thompson's group F satisfies the property if and only if it is non-amenable, therefore giving a computability characterization of this well-known open problem. Joint work with Mathieu Sablik and Ville Salo.

**February 3:**Julien Melleray (Université Lyon 1)

**Title:**From invariant measures to orbit equivalence, via locally finite groups

**Abstract:**A famous theorem of Giordano, Putnam and Skau (1995) states that two minimal homeomorphisms of a Cantor space X are orbit equivalent (i.e, the equivalence relations induced by the two associated actions are isomorphic) as soon as they have the same invariant Borel probability measures. I will explain a new "elementary" approach to prove this theorem, based on a strengthening of a result of Krieger (1980). I will not assume prior familiarity with Cantor dynamics. This is joint work with S. Robert (Lyon).

**February 10:**Lauren Wickman (University of Florida)

**February 17:**Social Hour

**February 24 at 10:00 AM:**Jan Moritz Petschick (Heinrich Heine University Düsseldorf)

**Title:**Groups of small period growth

**Abstract:**The concept of period growth was defined by Grigorchuk in the 80s, but still there are only a few examples of groups where we can estimate this invariant. We will sketch a connection to the Burnside problems and introduce a family of groups with very small period growth, answering a question by Bradford.

**March 3 (combined with the Probability Seminar):**

**March 10:**Yan Mary He (University of Oklahoma)

Spring 2022

**March 31:**Andy Zucker (University of California San Diego)

**April 7:**

**April 14:**

**April 21:**

**April 28:**

**May 5:**Robin Tucker-Drob (University of Florida)

**May 12:**

**May 19:**

**May 26:**Dami Lee (University of Washington)

**June 2:**Calgar Uyanik (University of Wisconsin)