# SCIENTIFIC PROGRAMS AND ACTIVITIES

May 18, 2013
THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
20th ANNIVERSARY YEAR

Set                    Theory and C*-algebras Seminar Logic and Operator Algebras                   Fields                    Institute, Room 210                    (Map)                             10:00 - 11:30 a.m.                                      Organizers:                    Ilijas Farah (York University), Juris Steprans (York University),                    Bradd Hart (McMaster University)

### OVERVIEW

This weekly seminar is devoted to applications of logic to operator algebras. In its first semester it will feature three types of talks: (i) introductory talks on operator algebras aimed at logicians, (ii) introductory talks on logic aimed at operator algebraists and (iii) discussions of recent applications of set theory and model theory to C*-algebras and von Neumann algebras.
In addition to these, some of the meetings will be 'working seminars' devoted to addressing open problems or working through the literature.

Upcoming Seminars

TBA

Past Seminars 2012-13
Mar. 26

Dave Penneys
GJS C*-algebras

Guionnet-Jones-Shlyakhtenko (GJS) gave a diagrammatic proof of a result of Popa which reconstructs a subfactor from a subfactor planar algebra. In the process, certain canonical graded *-algebras with traces appear. In the GJS papers, they show that the von Neumann algebras generated by the graded algebras are interpolated free group factors. In ongoing joint work with Hartglass, we look at the
C * -algebras generated by the graded algebras. We are interested in a connection between subfactors and non-commutative geometry, and the first step in this process is to compute the K-theory of these C * -algebras. I will talk about the current state of our work.

Mar. 21

Makoto Yamashita
Deformation of algebras from group 2-cocycles

Algebras with graded by a discrete can be deformed using 2-cocycles on the base group. We give a K-theoretic isomorphism of such deformations, generalizing the previously known cases of the theta-deformations and the reduced twisted group algebras. When we perturb the deformation parameter, the monodromy of the Gauss-Manin connection can be identified with the action of the group cohomology.

Mar. 5

Danny Hay

Feb. 28

Martino Lupini
C*-algebras and omytting types

I will give an introduction to model theory for operator algebras. I will then explain how many important classes of C*-algebras can be characterized by the model-theoretic notion of omitting types. I will conclude presenting some applications to the theory of UHF and AF algebras.

Jan. 14

Martino Lupini
Logic, ultraproducts and central sequence algebras

I will introduce the fundamental notions of the logic for metric structures, among which the notiond of ultraproduct. I will then describe and study in this framework the notion of central sequence algebra of a unital C*-algebra, in particular in relation to its applications in the paper "CENTRAL SEQUENCE C*-ALGEBRAS AND TENSORIAL ABSORPTION OF THE JIANG-SU ALGEBRA"

Dec 19 Bradd Hart, McMaster University
Model theory and operator algebra

The title is a catch all for the thesis that these two subjects have something to do with one another. I will try to make this point by looking at the state of our knowledge of the continuous theory of the hyperfinite II_1 factor and its relationship with the Connes Embedding Problem.

Dec 12 Dave Penneys
II_1 factors and subfactors 2

We will give a broad introduction to II_1 factors, starting with some basic facts, including standard form and the coupling constant. We will then focus on subfactors, and we will aim to discuss some classification results.
Dec 5 Dave Penneys

We will give a broad introduction to II_1 factors, starting with some basic facts, including standard form and the coupling constant. We will then focus on subfactors, and we will aim to discuss some classification results.
Nov 28

Paul McKenney (CMU)
Automorphisms of a corona algebra

I will discuss the automorphisms of $\ell^\infty(CAR) / c_0(CAR)$, and give an overview of the proof that, assuming Todorcevic's Axiom and Martin's Axiom, they are all trivial.
Nov 21

Saeed Ghasemi (York)
Tensor products of SAW* algebras

First I will introduce SAW*-algebras as non-commutative analogous of sub-Stonean spaces in topology and state some of the results about sub-Stonean spaces which have been generalized by G.K. Pedersen to SAW*-algebras. Secondly I will show that there is no surjective *-homomorphism from SAW*-algebras into tensor product of two infinite dimensional C*-algebras using the corresponding result for sub-Stonean spaces, i.e. SAW*-algebras are essentially non-factorizable.

Nov 14

No Seminar
Nov 7

Isaac Goldbring (UIC)
Pseudofinite and pseudocompact metric structures

In classical logic, an L-structure M is said to be pseudofinite if every L-sentence which is true in all finite L-structures is also true in M; equivalently, if an L-sentence is true in M, then it is true in some finite L-structure. The random graph is a pseudofinite structure and pseudofinite fields have proven to be very interesting to model theorists. In joint work with Vinicius Cifu Lopes, we initiate the study of pseudofinite metric structures (in the sense of continuous logic). Due to the lack of negations in continuous logic, the aforementioned equivalence doesn't hold, leading to two separate notions, which we call pseudofinite and strongly pseudofinite. By replacing finite structures by compact structures, we obtain the related notions of pseudocompact and strongly pseudocompact. In this talk, I will discuss some basic properties of these notions as well as many examples, including a connection with von Neumann algebras. I will also discuss some interesting open questions.

Oct. 16 &
Oct. 24
No seminar Oct. 16 due to Fields Medal Symposium

No seminar October 24 due to Workshop on Forcing Axioms and their Applications, October 22-26
Oct. 10

Martino Lupini (York)
Connes spectrum and inner automorphisms of C*-algebras

I will introduce the Connes spectrum for automorphisms of C*-algebras and explain how inner automorphisms can be characterized in terms of it.
Oct. 3

Martino Lupini (York)
Spectrum of one-parameter groups of automorphisms and derivations of C*-algebras

I will introduce the spectrum of a one-paramter group of automorphisms of a C*-algebra, and present its applications to the study of derivations. In particular, I will prove the result of Sakai that every derivation of a simple C*-algebra is inner, and the result of Akemann, Elliott, Pedersen and Tomiyama that every derivation of a separable C*-algebra with continuous trace is inner.

Sept. 26

Tristan Bice (Fields Institute and York)
General applications of set theory to C*-algebras
Sept. 19
Aaron Tikuisis (University of Muenster)
Nuclear dimension and decomposition rank

Sept. 5

Luis Santiago ( University of Oregon)
Jiang-Su algebra

Aug. 29

Zhiqiang Li (University of Toronto)
A basic introduction to KK-theory of C*-algebras

I will present some basic facts about KK-groups, and show calculation of some concrete examples.

Aug. 22
1:30 p.m.

Henning Petzka (University of Toronto)
The Bott projection in the classification of C*-algebras

Vector bundles and Chern classes have been used to construct C*-algebras with rather exotic behavior. In particular, the Bott projection has played a prominent role. We will look on some constructions of `exotic' C*-algebras, - for instance Rordam's simple C*-algebra containing both a finite and a (non-zero) infinite projection,- and the unifying idea behind their constructions.

Aug. 15

Jorge Plazas ( Fields Institute)
An Introduction to Noncommutative Geometry

Noncommutative geometry, largely based on the theory operator algebras, extends the tools of geometry beyond their classical scope leading to deep insights and applications in various areas of mathematics. In this talk we will give a short review of some of the key ideas of the field, introduce some of its techniques and discuss a few examples.

Aug. 8

Luis Santiago (University of Oregon)
An Introduction to Cuntz Semigroup

Aug 1, 2012

Zhiqiang Li
Introduction to KK-theory
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