### Complex Geometry and Operator Theory

- Series
- School of Mathematics Colloquium
- Time
- Tuesday, February 14, 2012 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Ron Douglas – Texas A&amp;M University

An intesting class of bounded operators or algebras of bounded operators
on Hilbert spaces, particularly on Hilbert spaces of holomorphic
functions, have a natural interpretation in terms of concepts from
complex geometry. In particular, there is an intrinsic hermitian
holomorphic vector bundle and many questions can be answered in terms of
the Chern connection and the associated curvature.
In this talk we describe this setup and some of the results obtained
in recent years using this approach. The emphasis will be on concrete
examples, particularly in the case of Hilbert spaces of holomorphic
functions such as the Hardy and Bergman spaces on the unit sphere in
C^n.