Joint Colloquium: Sukochev -- Non-commutative analysis and geometry

Speaker: Prof.  Fedor A Sukochev (UNSW) 

Title: Noncommutative analysis and geometry 

Date: Friday, 10 October 2008 Time: 2:00 pm Venue: Room 373 Carslaw Building, University
of Sydney 

Lunch plans: We will meet for lunch at 12:30 PM just outside the main entrance to
Carslaw on the second floor.  Please let me know if you plan to join us.  

Abstract: 

Noncommutative analysis applies abstract methods of Banach space theory to spaces that
naturally appear in operator theory.  In the recent past, noncommutative analysis (in a
wide sense) has developed rapidly because of its interesting and fruitful interactions
with classical theories such as C* and W*-algebras, Banach spaces, probability, harmonic
analysis.  Important recent advance in the differential calculus of functions of
non-commuting operators has very recently led to new analytic formulae for the spectral
flow along a smooth path of self-adjoint Breuer-Fredholm operators in a semi-finite von
Neumann algebra.  These analytic formulae for spectral flow of bounded/unbounded
Breuer-Fredholm operators fit into the overall picture in noncommutative geometry and
settle an issue which may be traced back to the 1974 Vancouver ICM address of I.  M.
Singer.  This latter result is obtained jointly with A.  Carey and D.  Potapov.