Inperson 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
Fall 2023 Speakers Past Speakers

Oct. 3 (Tuesday): Amanda Wilkens (University of Texas, Austin)
Location: AP&M 7218 and Zoom
Title: PoissonVoronoi tessellations and fixed price in higher rank
Abstract:
We overview the cost of a group action, which measures how much
information is needed to generate its induced orbit equivalence
relation, and the ideal PoissonVoronoi tessellation (IPVT), a new
random limit with interesting geometric features. In recent work, we
use the IPVT to prove all measure preserving and free actions of a
higher rank semisimple Lie group on a standard probability space have
cost 1, answering Gaboriau's fixed price question for this class of
groups. We sketch a proof, which relies on some simple dynamics of the
group action and the definition of a Poisson point process. No prior
knowledge on cost, IPVTs, or Lie groups will be assumed. This is joint
work with Mikolaj Fraczyk and Sam Mellick.
video
 Oct. 12: Petr Naryshkin (WWU M?nster)
Location: AP&M 7321 and Zoom
Title: Borel asymptotic dimension of the boundary action of a hyperbolic group
Abstract:
We give a new short proof of the theorem due to Marquis and Sabok,
which states that the orbit equivalence relation induced by the action
of a finitely generated hyperbolic group on its Gromov boundary is
hyperfinite. Our methods permit moreover to show that every such action
has finite Borel asymptotic dimension. This is a joint work with Andrea
Vaccaro.
 Oct. 19: Koichi Oyakawa (Vanderbilt University)
Location: AP&M 7321
Title: Hyperfiniteness of boundary actions of acylindrically hyperbolic groups
Abstract:
A Borel equivalence relation on a Polish space is called hyperfinite if
it can be approximated by equivalence relations with finite classes.
This notion has long been studied in descriptive set theory to measure
complexity of Borel equivalence relations. Although group actions on
hyperbolic spaces don't always induce hyperfinite orbit equivalence
relations on the Gromov boundary, some natural boundary actions were
recently found to be hyperfinite. Examples of such actions include
actions of hyperbolic groups and relatively hyperbolic groups on their
Gromov boundary and acylindrical group actions on trees. In this talk,
I will show that any acylindrically hyperbolic group admits a
nonelementary acylindrical action on a hyperbolic space with
hyperfinite boundary action.
 Oct. 26: Christopher Shriver (University of Texas, Austin)
Location: AP&M 7321
Title: Sofic entropy, equilibrium, and local limits of Gibbs states
Abstract:
I will introduce some interacting particle systems on finite graphs and
Cayley graphs of countable groups, and discuss how sofic entropy helps
understand them.
More specifically, we consider two notions of statistical equilibrium:
an "equilibrium state" maximizes a functional called the pressure while
a "Gibbs state" satisfies a local equilibrium condition. On amenable
groups (for example, integer lattices) these notions are equivalent,
under some assumptions on the interaction. Barbieri and Meyerovitch
have recently shown that one direction holds for general sofic groups:
equilibrium states are always Gibbs.
I will show that the converse fails in the simplest nontrivial case:
the free boundary Ising state on a free group (an infinite regular
tree) is Gibbs but not equilibrium. I will also discuss what this says
about Gibbs states on finite locallytreelike graphs: it is wellknown
that their local statistics are described by some Gibbs state on the
infinite tree, but in fact they must locally look like a mixture of
equilibrium states. This constraint can be used to compute local limits
of finitary Gibbs states for a few interactions.
 Nov. 2: Forte Shinko (UC Berkeley)
Location: AP&M 7321
Title: Hyperfiniteness of generic actions on Cantor space
Abstract:
A countable discrete group is exact if it has a free action on Cantor
space which is measurehyperfinite, that is, for every Borel
probability measure on Cantor space, there is a conull set on which the
orbit equivalence relation is hyperfinite. For an exact group, it is
known that the generic action on Cantor space is measurehyperfinite,
and it is open as to whether the generic action is hyperfinite; an
exact group for which the generic action is not hyperfinite would
resolve a longstanding open conjecture about whether
measurehyperfiniteness and hyperfiniteness are equivalent. We show
that for any countable discrete group with finite asymptotic dimension,
its generic action on Cantor space is hyperfinite. This is joint work
with Sumun Iyer.
 Nov. 9: Itamar Vigdorovich (Weizmann Institute)
Location: Zoom
Title: Stationary dynamics on character spaces and applications to arithmetic groups
Abstract:
To any group G is associated the space Ch(G) of all characters on G.
After defining this space and discussing its interesting properties,
I'll turn to discuss dynamics on such spaces. Our main result is that
the action of any arithmetic group on the character space of its
amenable/solvable radical is stiff, i.e, any probability measure which
is stationary under random walks must be invariant. This generalizes a
classical theorem of Furstenberg for dynamics on tori. Relying on works
of Bader, Boutonnet, Houdayer, and Peterson, this stiffness result is
used to deduce dichotomy statements (and 'charmenability') for higher
rank arithmetic groups pertaining to their normal subgroups, dynamical
systems, representation theory and more. The talk is based on a joint
work with Uri Bader.
video
 Nov. 16: Elyasheev Leibtag (Weizmann Institute)
Location: Zoom
Title: Images of algebraic groups and mixing properties
Abstract:
Let G be an algebraic group over a local field. We will show that the
image of G under an arbitrary continuous homomorphism into any
(Hausdorff) topological group is closed if and only if the center of G
is compact. We will show how mixing properties for unitary
representations follow from this topological property.
video
 Nov. 30: Ferrán Valdez (National Autonomous University of Mexico, Morelia)
Location: AP&M 7321
Title: Big mapping class groups
Abstract:
In this talk we will introduce big mapping class groups and compare them to classical mapping class groups. The goal of the talk is to convince you that big MCGs form an interesting class of Polish groups.
 Dec. 7: Zuo Lin (UCSD)
Location: AP&M 7321
Winter 2024
 Jan. 11: Pieter Spaas (University of Copenhagen)
 Jan. 18:
 Jan. 25: Jane Wang (University of Maine)
 Feb. 1 (4:00 pm): Jinho Jeoung (Seoul National University)
 Feb. 8:
 Feb. 15:
 Feb. 22:
 Feb. 29:
 March 7:
 March 14: