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

Introduction to KK-theory (and its categorical properties)

by Abhijnan Rej | Fields Institute
Time: 16:10  (Monday, Feb. 01, 2010)
Location: BA6183, Bahen Center, 40 St. George Street
Abstract:
After taking care of some notions related to higher K-theory of C*-algebras, I introduce KK-theory. I also describe the categorical underpinnings of Kasparov's construction and show how KK-theory specializes to both K-theory and K-homology. I conclude with some basics of the theory of extensions and crossed products (needed for later!), following Blackadar's exposition. http://sites.google.com/site/abhijnanrej/stringsncg

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)