Operator Theory Seminar

This seminar, organized by Man-Duen Choi, Chandler Davis, George Elliott, and Peter Rosenthal, is devoted, loosely speaking, to the study of all areas of mathematics involving Hilbert space operators. (This has variously been interpreted recently to include matrix theory, index theory of differential operators and other aspects of non-commutative geometry, invariant subspace theory, quantum information theory, C*-algebra classification theory, and string theory.)


 

Details

Characterizing $\mathcal{Z}$-Stable $C^*$-algebras

by Danny Hay | University of Toronto
Time: 16:10  (Monday, Mar. 19, 2012)
Location: BA6183, Bahen Center, 40 St George St
Abstract:
It is thought that a regularity condition known as $\mathcal{Z}$-stability is the missing ingredient needed for a simple, nuclear $C^*$-algebra to be classifiable in the sense of Elliott. Toms and Winter have conjectured that for simple, unital, nuclear, separable $C^*$-algebras, $\mathcal{Z}$-stability may be equivalent to two other regularity conditions: finite nuclear dimension (a sort of noncommutative topological dimension), and strict comparison of positive elements. This conjecture was recently verified in the case of AH algebras, and some of the details of this result will be discussed. The possibility of generalizing this result to ASH algebras will also be considered.

Dates in this series

· Monday, Jan. 25, 2010: K-theory of C*-algebras and KK-theory (Abhijnan Rej)
· Monday, Feb. 01, 2010: Introduction to KK-theory (and its categorical properties) (Abhijnan Rej)
· Monday, Feb. 08, 2010: The intersection product in KK-theory and non-commutative topology (Abhijnan Rej)
· Monday, Feb. 22, 2010: D-branes and KK groups (Abhijnan Rej)
· Monday, Mar. 22, 2010: Relative determinants and isospectrality on surfaces with cusps (Clara Aldana)
· Monday, Mar. 29, 2010: The Cuntz semigroup of C(X,A) where A is a simple AF C*-algebra (Aaron Tikuisis)
· Monday, Apr. 05, 2010: Basis map operators arising from regular semigroup representations (Barry Rowe)
· Monday, Apr. 19, 2010: On the classification of C*-algebras (Henning Petzka)
· Monday, May. 10, 2010: The Dirac operator on the noncommutative space of connections (Alan Lai)
· Tuesday, May. 11, 2010: Naimark extensions for indeterminacy in the moment problem (Franek Szafraniec)
· Monday, May. 31, 2010: On triangular factorization of positive operators (Lev A. Sakhnovich)
· Monday, Sep. 20, 2010: Quantum error correction, and higher rank numerical ranges of normal matrices (Chi-Kwong Li)
· Friday, Jan. 14, 2011: Spectral zeta functions and Gauss-Bonnet type theorems in noncommutative geometry (Masoud Khalkhali)
· Monday, Feb. 07, 2011: Group actions and noncommutative geometry (Raphael Ponge )
· Monday, Mar. 07, 2011: On certain multiplier projections (Henning Petzka)
· Monday, Mar. 14, 2011: What are quantum channels through my old dream? (Man-Duen Choi)
· Monday, Mar. 21, 2011: The nuclear dimension of a C* algebra (Nicola Watson)
· Monday, Mar. 28, 2011: A generalization of the Weyl-von Neumann Theorem (Daniel Hay)
· Monday, Mar. 19, 2012: Characterizing $\mathcal{Z}$-Stable $C^*$-algebras (Danny Hay)
· Monday, Mar. 26, 2012: A stably finite $C^*$-algebra without bounded trace (Henning Petzka)
· Monday, Apr. 02, 2012: Decomposition rank, nuclear dimension and tracial approximation (Nicola Watson)
· Monday, Apr. 23, 2012: Hilbert Modules, Strong Morita Equivalence and Rotation Algebras (James Lutley)
· Monday, May. 28, 2012: Random Projections, Free Probability, and Holomorphic PDEs (Todd Kemp)
· Tuesday, Nov. 20, 2012: Universal C*-algebras of *-semigroups and the C*-algebra of a partial isometry (Berndt Brenken)
· Monday, Dec. 17, 2012: Constructing subfactors with jellyfish (Dave Penneys)