All talks will take place in Stevenson Center 1432, and all coffee breaks will be down the hall in Stevenson Center 1425.
8:30-9:00 | Coffee |
9:00-9:50 | Lewis Bowen |
10:00-10:30 | Coffee |
10:30-11:20 | Robin Tucker-Drob |
11:30-12:20 | Kostya Medynets |
12:30-2:00 | Lunch |
2:00-2:50 | Hanfeng Li |
3:00-3:30 | Coffee |
3:30-4:20 | Clinton Conley |
4:30-5:20 | Ionut Chifan |
8:30-9:00 | Coffee |
9:00-9:50 | Simon Thomas |
10:00-10:30 | Coffee |
10:30-11:20 | Artem Dudko |
11:30-12:20 | Kate Juschenko |
12:30-2:00 | Lunch |
2:00-2:50 | Thomas Sinclair |
3:00-3:50 | Darren Creutz |
Lewis Bowen |
Cheeger Constants and L² Betti Numbers The Cheeger constant of an infinite-volume manifold is the greatest lower bound of area to volume ratios of its compact sub-manifolds. It is related to the zero-th eigenvalue of the Laplace operator and, in the case of real hyperbolic manifolds, to the Hausdorff dimension of the limit set of the fundamental group. We ask: how small can the Cheeger constant be of a real hyperbolic n-manifold with no boundary and free fundamental group? I'll explain some partial results on this question by making use of L² Betti numbers. |
Ionut Chifan |
Structural Results for II₁ Factors of Negatively Curved Groups In this talk I will discuss some recent results on the classification of von Neumann algebras arising from negatively curved groups and their measure preserving actions on probability spaces. This is based on a joint work with T. Sinclair and B. Udrea. |
Clinton Conley |
Local Complexity Among Treeable Equivalence Relations Group-theoretic rigidity techniques such as Zimmer and Popa cocycle superrigidity have been instrumental in works of Adams-Kechris, Thomas, and Hjorth (among others) in realizing complexity in the partial order of Borel reducibility among countable Borel equivalence relations. We introduce an alternative elementary notion of rigidity which interacts favorably with Borel reducibility, allowing us to localize various complexity results to just above measure hyperfinite in the class of treeable equivalence relations. This is joint work with Ben Miller. |
Darren Creutz |
Stabilizers of Ergodic Actions of Product Groups and Lattices in Products
The Margulis Normal Subgroup Theorem states that any normal subgroup of
an irreducible lattice in a center-free higher-rank semisimple Lie group
is of finite index. Stuck and Zimmer, expanding on Margulis' approach,
showed that any properly ergodic probability-preserving ergodic action
of a semisimple real Lie group with every simple factor of higher-rank
is essentially free and likewise for lattices in such groups. Bader and
Shalom, following a different approach, showed that any properly ergodic
action of a product of two simple groups with property (T) is
essentially free, but their methods do not yield information about
lattices. |
Artem Dudko |
On Characters of Approximately Finite Groups and the Higman-Thompson Groups It is well-known that given a measure-preserving action of a group G on a measure-space (X,μ) the formula χ(g)=μ{x : gx=x} defines a character on G. Vershik conjectured that for a “rich” group G all characters can be obtained in this way. We verify Vershik’s conjecture for approximately finite groups (full groups of Bratteli diagrams) and the Higman-Thompson groups. The talk is based on joint papers with Konstantin Medynets. |
Kate Juschenko |
On Klondike of Amenable Groups I will discuss amenable and recurrent actions of discrete groups. Sufficient conditions of amenability of a finitely generated group acting by homeomorphisms on a topological space will be presented. Surprisingly, this conditions are satisfied by large classes of groups: all known non elementary amenable groups, bounded and linearly growing automata groups. This is joint with V. Nekrashevych and M. de la Salle. |
Hanfeng Li |
Mean Dimension and von Neumann-Luck Rank Mean dimension is a numerical invariant for continuous actions of countable amenable groups, coming up in topological dynamics and related to entropy. The von Neumann-Luck rank is an invariant for modules of the integral group ring of countable groups, coming up in L²-invariants and related to L²-Betti numbers. I will discuss the relation between the von Neumann-Luck rank of a module of the integral group ring of a countable amenable group and the mean dimension of the associated algebraic action. This is joint work with Bingbing Liang. |
Kostya Medynets |
Full Groups in Ergodic Theory We will give an overview of the properties of full groups of ergodic measure-preserving equivalence relations. We will discuss the algebraic structure of full groups and its relation to the dynamical properties of the underlying equivalence relations. |
Thomas Sinclair |
Some Comments on Ergodic Theorems for Affine Actions on Hilbert Space
|
Simon Thomas |
Invariant Random Subgroups of the Group of Finitary Permutations I will discuss Vershik's classification of the invariant random subgroups of the group of finitary permutations of the natural numbers. |
Robin Tucker-Drob |
Mixing Actions of Countable Groups are Almost Free
A measure preserving action of a countably infinite group G is called
totally ergodic if every infinite subgroup of G acts ergodically. For
example, all mixing and mildly mixing actions are totally ergodic. I
will discuss the proof that all totally ergodic actions are free modulo
a finite kernel. |
Funding for the workshop is in part from the Shanks Foundation (Vanderbilt University).