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

The Dirac operator on the noncommutative space of connections

by Alan Lai | University of Toronto
Time: 16:10  (Monday, May. 10, 2010)
Location: BA6183, Bahen Center, 40 St George St
Abstract:
In attempts to combine Noncommutative Geometry and Loop Quantum Gravity, Aastrup-Grimstrup-Nest constructed a spectral triple (B,H,D) over a space of connections. AGN showed that their spectral triple includes a representation of the Poisson algebra of General Relativity, and the Dirac operator D resembles the area operator in LQG to some extent. As we will see, AGN's spectral triple is obtained via a certain limiting process. In this process, D depends on a set of non-canonical data, which can be thought of as weight assignments. We will study this set of weight assignments using the Chern character of Jaffe-Lesniewski-Osterwalder.

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)