Woensdag 9 juli 2008
||Fedor Sukochev (Flinders University Adelaide)
||The spectral shift function and spectral flow
||11:00 - 12:00
Vanaf kwart voor 11 is er koffie en thee in de binnenstraat
(voor de zaal).
Spectral flow is normally associated with paths of operators with
discrete spectrum such as Dirac operators on compact manifolds.
In this case, Atiyah and Lusztig have defined the spectral flow of a continuous
path in the space of all self-adjoint Fredholm operators to be the number of
eigenvalues (counted with multiplicities) which pass through 0
positive direction minus the number which pass through 0
in the negative
direction as one moves from the initial point of the path to the final point.
Until about a decade ago, spectral flow was considered primarily in topological
terms and there seemed to be no analytical viewpoint. In this talk we explain
how one can view spectral flow as the integral of a one-form (this viewpoint is
mostly due to the efforts by Getzler, Carey and Phillips) and show a connection
with another classical notion in the operator theory, namely with the spectral
shift function of M.G. Krein.