Contact Info
Pure MathematicsUniversity of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada
N2L 3G1
Departmental office: MC 5304
Phone: 519 888 4567 x33484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
Visit our COVID-19 information website to learn how Warriors protect Warriors.
Please note: The University of Waterloo is closed for all events until further notice.
In B(H) (the set of bounded operators on a Hilbert space), the spectral flow counts the net number of eigenvalues which change sign as one travels along a path of self-adjoint Fredholm operators. The ability to calculate the spectral flow allows one to calculate the Fredholm index of some operators, making it of interest in the study of noncommutative geometry. It is possible to generalize the concept of spectal flow to a semifinite von Neumann algebra, as we can use a trace on the algebra to measure the amount of spectrum which changes sign.
Lesch showed in the type I case (i.e. B(H)) that a map on a suitable set of paths which satisfies three fairly straight-forward conditions is the spectral flow map. In this talk, I will describe how Lesch's ideas can be modified to obtain a characterization of spectral flow in a type II factor.
Departmental office: MC 5304
Phone: 519 888 4567 x33484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Indigenous Initiatives Office.