UC San Diego Group Actions Seminar

In-person meetings are held in AP&M 7321 and Zoom meetings are held here.

If you would like to be included or removed from our email announcements, please email Brandon Seward.

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

Current Quarter      Past Quarters

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• 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.
  
  video
  
  
• 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).
  
  video
  
  
• February 10: Lauren Wickman (University of Florida)
  
  Title: Knaster Continua and Projective Fraïssé Theory
  
  Abstract: The Knaster continuum, also known as the buckethandle, or the Brouwer–Janiszewski–Knaster continuum can be viewed as an inverse limit of 2-tent maps on the interval. However, there is a whole class (with continuum many non-homeomorphic members) of Knaster continua, each viewed as an inverse limit of p-tent maps, where p is a sequence of primes. In this talk, for each Knaster continuum K, we will give a projective Fraïssé class of finite objects that approximate K (up to homeomorphism) and examine the combinatorial properties of that the class (namely whether the class is Ramsey or if it has a Ramsey extension). We will give an extremely amenable subgroup of the homeomorphism group of the universal Knaster continuum.
  
  video
  
  
• February 24 at 10:00 AM: J. 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.
  
  video
  
  
• March 3 (joint with Probability Seminar) at 3:00 PM: Tom Hutchcroft (California Institute of Technology)
  
  Location: AP&M 6402 and on Zoom
  
  Title: The Ising model on nonamenable groups
  
  Abstract: I will outline a proof that the Ising model has a continuous phase transition on any nonamenable Cayley graph. This will involve some neat probabilistic applications of ergodic-theoretic machinery such as factors of IID and the spectral theory of group actions. I will aim to make the talk accessible to a broad community.
  
  video
  
  
• March 10: Yan Mary He (University of Oklahoma)
  
  Location: AP&M 7218 and on Zoom
  
  Title: A quantitative equidistribution of angles of multipliers of hyperbolic rational maps
  
  Abstract: In this talk, we will consider the angular component of multipliers of repelling cycles of a hyperbolic rational map in one complex variable. Oh-Winter have shown that these angles of multipliers uniformly distribute in the circle (-\pi, \pi]. Motivated by the sector problem in number theory, we show that for a fixed $K \geq 1$, almost all intervals of length 2\pi/K in (-\pi, \pi] contains a multiplier angle with the property that the norm of the multiplier is bounded above by a polynomial in K. This is joint work with Hongming Nie.
  
  video