Conferences and Seminars I was at in 2009

Date: 2/6/09
 Subfactor Seminar,
at Vanderbilt University.
 Title: Derivations on groupmeasure space constructions
 Abstract:
In this talk we will investigate the structure of a class of closable derivations on von Neumann algebras coming from groupmeasure space constructions.
We will then show how to apply these results to obtain new examples of von Neumann algebras which do not arise as groupmeasure space constructions,
for example the von Neumann algebra L( SL(3, Z) * G ) where G is any nontrivial group.
 Notes

Date: 3/15/09  3/18/09
 Von Neumann Algebras and Ergodic Theory,
at UCLA.
 Title: A class of II_{1} factors with unique groupmeasure space decomposition
 Abstract:
We show that if G is a countable discrete group which contains an ICC subgroup with relative property (T) and has an unbounded
cocycle into a C_{0}representation (e.g. SL(3, Z) * H where H is any nontrivial group) then any measure preserving,
free, ergodic, profinite action of G on a standard probablility space gives rise to a II_{1} factor with unique
groupmeasure space Cartan subalgebra. Also, if G is ICC then we show that LG x N is not a groupmeasure space construction
whenever N is a finite factor with the Haagerup property.

Date: 4/22/09
 Topology & Group Theory Seminar,
at Vanderbilt University.
 Title: \ell^2Betti numbers.
 Abstract:
This will be an introductory talk on \ell^2Betti numbers for groups. I will define what \ell^2Betti numbers are and discuss basic examples and properties.
I will then discuss some applications and open problems for \ell^2Betti numbers in the areas of ergodic theory and von Neumann algebras.

Date: 6/28/09  7/3/09
 Affine Isometric Actions of Discrete Groups,
at ETH Zürich.
 Title:Virtual W*Esuperrigidity.
 Abstract:
Rigidity results, in their most common form is when a "weak equivalence" between two objects must come from an identification of the objects.
Associated to a countable group acting by measure preserving transformations on a probability space is a finite von Neumann algebra (W*algebra).
Two group actions are said to be W*Equivalent if the corresponding von Neumann algebras are isomorphic.
We will present a rigidity result showing that in in some cases W*Equivalence implies a stronger form of equivalence (Orbit Equivalence).
Combining this with results of Ioana, Ozawa, and Popa we will produce examples of group actions for which the von Neumann algebra virtually remembers both the group and the action.

Date: 8/3/09  8/7/09
 Concentration Week on Operator Spaces and Approximation Properties of Discrete Groups,
Workshop in Analysis and Probability
at Texas A&M University
 Title: Applications of closable derivations in the theory of II_{1} factors
 Lecture 1: Approximation properties of closable derivations, quantum Dirichlet forms, and completely positive semigroups.
 Abstract:
In this talk we will explain the connection established by Sauvageot between closable derivations, quantum Dirichlet forms,
and completely positive semigroups. We will also introduce the key approximation properties needed in order to exploit the
bimodule structure of the correspondences in which our derivations map into.
 Lecture 2: L^{2}rigidity. Primality and solidity for II_{1} factors.
 Abstract:
In this talk we introduce the notion of L^{2}rigidity for II_{1} factors and show how this leads to examples
of prime II_{1} factors. We will also show a Kurosh type theorem for L^{2}rigid subalgebras of free products
and we will give a proof of Ozawa's result that the free group factors are solid.
 Lecture 3: II_{1} factors which do not arise as groupmeasure space constructions.
 Abstract:
In this talk we will show a "proper/bounded" dichotomy type result for derivations on groupmeasure space constructions which
map into compact correspondences. We will use this to give new examples of II_{1} factors which do not arise as
groupmeasure space constructions, for example the group von Neumann algebra L(SL(n, Z) * G) where n > 2 and G is any
nontrivial group.

Date: 8/17/09  8/21/09

Date: 11/7/09  11/8/09
 Special Session on Operator Algebras,
AMS Sectional Meeting,
at UC Riverside.
 Title: Cocycle Superrigidity for Gaussian Actions.
 Abstract:
I will present a general setting to prove $U_{fin}$cocycle superrigidity for Gaussian actions in terms of closable derivations on von Neumann algebras.
In this setting I will provide new examples of this phenomenon, extending results of S. Popa. I will also use a result of K. Schmidt to give a necessary
cohomological condition on a group representation in order for the resulting Gaussian action to be $U_{fin}$cocycle superrigid.
This is joint work with Thomas Sinclair.

Date: 12/8/09  12/11/09
 Operators and Operator Algebras,
Conference in Honor of Alastair Gillespie and Allan Sinclair
at The University of Edinburgh.
 Title: Examples of group actions which are W*Esuperrigid.
 Abstract:
An essentially free measure preserving action of a group on a standard probability space is called W*Esuperrigid if the groupmeasure space
construction of Murray and von Neumann completely remembers the structure of the group and the action.
In my talk I will give some examples of this phenomenon.

Date: 12/16/09  12/20/09
 Joint Meeting of the Korean Mathematical Society and
the American Mathematical Society,
Special Session on Operator Theory and Operator Algebras,
at Ewha Womans' University in Seoul, South Korea.
 Title: Examples of group actions which are W*Esuperrigid.
 Abstract:
An essentially free measure preserving action of a group on a standard probability space is called W*Esuperrigid if the groupmeasure space
construction of Murray and von Neumann completely remembers the structure of the group and the action.
In my talk I will give some examples of this phenomenon.