June 16, 2009
Shoichiro Sakai
SPECIAL SEMINAR -- On the Kadison-Singer Problem

June 11, 2009
Shoichiro Sakai
SPECIAL SEMINAR -- On the Kadison-Singer Problem
The Kadison-Singer Problem is one of the outstanding problems in C*-algebra theory. When it was proposed in 1959, the proposers inclined to the view that the problem has a negative solution. Even today, many researchers are very actively studying the problem. The main reason is due to the fact that the problem is equivalent to many important open problems of several branches in mathematics, applied mathematics and engineering. I think this problem might be closely related to the axiomatic set theory of operator algebras.
Because of recent remarkable progress in the axiomatic set theory of operator algebras, I would like to present some considerations of the problem and related problems which may be interesting from the point of view of axiomatic set theory in operator algebras.

May 14, 2009
Benoît Jacob
Talk on his most recent work

May 12, 2009
Working Seminar

May 7, 2009
Greg Maloney, University of Toronto
Talk on his most recent work

May 5, 2009
Aaron Tikuisis
The Cuntz Semigroup for Commutative C*-algebras whose Spectrum has Dimension At Most Three
In my most recent talk, I gave a description of the Cuntz semigroup for C(X) where X is a compact metric space with imension at most three (a result of joint work with Leonel Robert). Today I will continue the proof of this description. As an application of the description, I will show these Cuntz semigroups have weak cancellation.

April 30, 2009
Greg Maloney, University of Toronto
Talk on his most recent work

April 28, 2009
Greg Maloney, University of Toronto
Talk on his most recent work

April 23, 2009
Leonel Robert
Talk on his most recent work

April 21, 2009
Teodor Banica
Half-liberated quantum groups
I will present some recent work, mostly in preparation, concerning the "second generation" of free quantum groups: the half-liberated ones. These appear by replacing the commutation relations ab=ba with the some weaker relations, of type abc=cba. This leads to some quite interesting combinatorics, currently under investigation (with Speicher, and with Vergnioux, Goswami, Curran..). One important change with respect to the "first generation" examples is that we are now very close to the classical case: for instance the corresponding algebras might be nuclear/amenable, which might make them fit into the general classification program for C^*-algebras.

April 16, 2009
Working Seminar

April 14, 2009
Fernando Mortari
Talk on his most recent work

April 9, 2009
Greg Maloney, University of Toronto
Talk on his most recent work

April 7, 2009
Aaron Tikuisis
Talk on his most recent work

April 2, 2009
Leonel Robert
Talk on his most recent work

March 31, 2009
Fernando Mortari
Talk on his most recent work

March 26, 2009
Benoît Jacob
Talk on his most recent work

March 24, 2009
Barry Rowe
Talk on his most recent work

March 19, 2009
Greg Maloney, University of Toronto
Talk on his most recent work

March 10, 2009
Aaron Tikuisis
Talk on his most recent work

March 5, 2009
Greg Maloney, University of Toronto
Talk on his most recent work

March 3, 2009
Greg Maloney, University of Toronto
Talk on his most recent work

February 26, 2009
Working Seminar

February 24, 2009
Greg Maloney, University of Toronto
Talk on his most recent work

February 19, 2009
Greg Maloney, University of Toronto
Talk on his most recent work

February 17, 2009
Working Seminar

February 12, 2009
Benoît Jacob
Talk on his most recent work

February 10, 2009
Greg Maloney, University of Toronto
Talk on his most recent work

February 5, 2009
Andrew Toms
Talk on his most recent work

February 3, 2009
Fernando Mortari
Talk on his most recent work

January 29, 2009
Aaron Tikuisis
Exploring the Cuntz Semigroup for Commutative C*-algebras
Elements of the Cuntz semigroup of a C*-algebra may be represented either by positive elements or by (finitely generated) Hilbert modules. The relationship between these two is fairly transparent in the case of a commutative algebra, and it seems that the most elucidating thing to do is to use lower semicontinuous projection-valued functions to represent elements of the Cuntz semigroup. I will discuss what a well supported element is in this context. I will also outline a proof, using lower semicontinuous projections, of the radius of comparison result (which was mentioned in my last talk). While at heart, this proof is no different than the one using positive elements (which I partially presented in my last talk), it is at times more transparent.

January 27, 2009
Luis Santiago
Talk on his most recent work

January 22, 2009
Leonel Robert
Talk on his most recent work

January 20, 2009
Fernando Mortari
Talk on his most recent work

January 15, 2009
Aaron Tikuisis
Radius of Comparison for C(X)
The radius of comparison of (the Cuntz semigroup of) a C*-algebra quantifies the extent to which elements of the Cuntz semigroup are comparable when they the application of lower semicontinuous states suggests that they should be comparable. This invariant is intimately related to perforation, since for many algebras, the Cuntz semigroup is weakly unperforated if and only if its radius of comparison is zero. In this talk, I will demonstrate that the radius of comparison of C(X) is bounded linearly by the dimension of X. This proof is largely an application of the concept of well-supported elements. An important corollary is that, in contrast to certain Villadsen algebras, simple unital AH algebras of slow dimension growth have almost unperforated Cuntz semigroups.

January 13, 2009
Greg Maloney, University of Toronto
Talk on his most recent work

January 8, 2009
Leonel Robert
Talk on his most recent work

January 6, 2009
Greg Maloney, University of Toronto
Talk on his most recent work

December 11, 2008
Greg Maloney, University of Toronto
Talk on his most recent work

December 9, 2008
Branimir Cacic
Talk on his most recent work

December 4, 2008 (*Postponed*)
Aaron Tikuisis
Radius of Comparison for C(X)
The radius of comparison of (the Cuntz semigroup of) a C*-algebra quantifies the extent to which elements of the Cuntz
semigroup are comparable when they the application of lower semicontinuous states suggests that they should be comparable. This invariant is intimately related to perforation, since for many algebras, the Cuntz semigroup is weakly unperforated if and only if its radius of comparison is zero.
In this talk, I will demonstrate that the radius of comparison of C(X) is bounded linearly by the dimension of X. This proof is largely an application of the concept of well-supported elements. An important corollary is that, in contrast to certain Villadsen algebras, simple unital AH algebras of slow dimension growth have almost unperforated Cuntz semigroups.

December 2, 2008
Fernando Mortari
Talk on his most recent work

November 27, 2008
Benoît Jacob
A Understanding Dixmier-Douady's first triviality theorem
We'll try together to understand how Dixmier and Douady's first triviality theorem works. This theorem states that any locally trivial bundle of Hilbert spaces, of constant infinite rank, over a paracompact base space, is trivial. This is in sharp contrast with the case of finite-dimensional vector bundles, as we all know many examples of non-trivial vector bundles. Dixmier and Douady's proof works by first associating to the bundle a "principal fibration" whose fiber is the unitary group of the Hilbert space fiber of the original bundle; in order to prove triviality of the original bundle it is enough to construct a global continuous section of the principal fibration, which is done by using the fact that the unitary group of an infinite- dimensional Hilbert space is contractible.
I also would like to discuss with you if and how these techniques could be extended to hilbert modules over noncommutative C*-algebras using the recent noncommutative Serre-Swan theorem by George Elliott and Katsunori Kawamura. For this part however, I am not knowledgeable at all and that would be like a working seminar.

November 25, 2008
Greg Maloney, University of Toronto
Talk on his most recent work

November 21, 2008
Barry Rowe
Talk on his most recent work

November 18, 2008
Barry Rowe
The Left Regular Representation of a Semigroup.
Given a semigroup S, we may consider the Hilbert space l_2(S) and for b in S define L_b as the induced operator from left multiplication of b on l_2(S). Natural questions to answer include what kind of conditions are needed on S to ensure that L_b is bounded, and what kind of operators L_b are possible. Also of interest is when the algebra generated by the left multiplication operators is reflexive.

November 13, 2008
Alin Ciuperca
Talk on his most recent work

November 11, 2008
Greg Maloney, University of Toronto
Talk on his most recent work

November 6, 2008
Leonel Robert
Talk on his most recent work

November 4, 2008
Aaron Tikuisis
The Cuntz Semigroup of C(X): Well-supported Approximants
I am trying to build an idea of what the Cuntz semigroup looks like for commutative C*-algebras. A promising idea seems to be looking at "well-supported" elements, as introduced by Andrew Toms. This talk will focus on the role of these elements.

October 30, 2008
Benoît Jacob
Some aspects of the state space of a C*-algebra
1) notions on states (Kadison function representation...)
2) notions on convex sets (faces, simplexes...)
3) some special simplexes embedded inside the state space (traces, KMS states)
4) faces in the state space
5) example of the compact operators K(H), in terms of Grassmannians
6) the oriented state space, and how it is an isomorphism invariant of C*-algebras.

October 28, 2008
Fernando Mortari
Talk on his most recent work

October 23, 2008
Andrew Toms, York University
Classification of C*-algebras associated to minimal uniquely ergodic homeomorphisms

October 21, 2008
Greg Maloney, University of Toronto
Talk on his most recent work

October 16, 2008
Julien Giol
Survey talk on hyperreflexivity and derivations.

October 14, 2008
Working Seminar

October 9, 2008
Working Seminar

October 7, 2008
Greg Maloney, University of Toronto
Talk on his most recent work

October 2, 2008
Working Seminar

September 30, 2008
Leonel Robert
Villadsen's constructions and the ones that followed

September 25, 2008
Greg Maloney, University of Toronto
Talk on his most recent work

September 23, 2008
Greg Maloney, University of Toronto
Talk on his most recent work

September 18, 2008
Aaron Tikuisis
Matrix Algebras over C*-algebras Generated by Stable Relations
When A is generated by weakly or strongly stable relations then so are matrix algebras over A. The proof of this fact will finally be completed in this talk. I will also discuss the question of whether this holds when instead of tensoring A by M_n, we tensor A y K, the algebra of compact operators. It turns out that even in the case A=C_0(0,1], which is projective, A \otimes K is not weakly semiprojective, so the answer is negative in the strongest sense.

September 16, 2008
Working Seminar

September 11, 2008
Aaron Tikuisis
Talk on his most recent work

September 9, 2008
Greg Maloney, University of Toronto
Talk on his most recent work

September 4, 2008
Aaron Tikuisis
Proving Stability
In showing that stability is preserved under direct sums and taking matrix algebras in the non-unital case, prototypical cases are C_0(0,1] \oplus C_0(0,1] and C_0(0,1] \otimes M_n. For these algebras, the property of projectivity will be demonstrated; this property is stronger than semiprojectivity. Of course, this property will be used in deriving the results mentioned above about stability being preserved by direct sum and matrix algebra constructions (although we probably won't yet get to the proof for the matrix algebra construction).

September 2, 2008
Working Seminar

August 28, 2008
Aaron Tikuisis
Proving Relations are Stable
We will revisit the constructions which produce generators and relations whose universal C*-algebra is the direct sum or the matrix algebra over the universal C*-algebra(s) of given generators and relations. We are tasked with showing that when the given generators and relations are weakly or exactly stable, the resulting relations have the same property. In doing so, we come across useful techniques for proving stability.

August 26, 2008
Working Seminar

August 21, 2008
Working Seminar

August 19, 2008
Aaron Tikuisis
Stability of C*-algebra Presentations
I will introduce the notions of weak and exact stability for a finite C*-algebra presentation <G|R>. The relationship between exact stability and semiprojectivity will be demonstrated and further properties of stable relations will be discussed.

August 14, 2008 -- 6180 of the Bahen building
Aaron Tikuisis
C*-Algebra Presentations
I will talk about the concept of C*-algebra generators and relations. We will see the construction of the universal C*-algebra associated to generators and relations, and some examples, (particularly examples of subalgebras of C[0,1] tensor M_n, and a technique for proving that these subalgebras are indeed equal to the universal C*-alg. for given generators and relations). This will lead up to ideas of stability for generators and relations, which I plan to discuss in follow up talk(s).

August 12, 2008
No Seminar

August 7, 2008
6180 of the Bahen building,
Nadish de Silva
Talk on his most recent work

August 5, 2008
No Seminar

July 31, 2008
Maria Grazia Viola
Talk on her most recent work

July 29, 2008
Kevin Teh
In this seminar, I'll present the derivation of the smooth functional calculus for spectral triples that satisfy the axioms of commutative geometry.

July 24, 2008
Working Seminar

July 22, 2008
Working Seminar

July 17, 2008
Greg Maloney, University of Toronto
Talk on his most recent work

July 15, 2008
Working Seminar

July 10, 2008
John Quigg, Arizona State
Coverings of skew-products and crossed products by coactions
Consider a projective limit G of finite groups G_n and a compatible family delta^n of coactions of the G_n on a C*-algebra A. From this data we obtain a coaction delta of G on A, and indicate how the coaction crossed product is isomorphic to a direct limit of the coaction crossed products of A by the delta^n.
If A = C*(Lambda) for some k-graph Lambda, and if the coactions delta^n correspond to skew-products of Lambda, then we can say more: the coaction crossed product may be realized as a full corner of the C*-algebra of a (k+1)-graph. Time permitting, I'll discuss connections with Yeend's topological higher-rank graphs and their C*-algebras.
This is joint work with David Pask and Aidan Sims.

SCIENTIFIC PROGRAMS AND ACTIVITIES

Operator Algebras Seminars July 2008 - June 2009

Operator Algebras Seminars
July 2008 - June 2009