Dr. Ronald Douglas, Distinguished Professor of Mathematics at Texas A&M University, will give a lecture Complex Geometry and Operator Theory at 3:30 pm in SR 207. A reception for Professor Douglas will take place at 3:00 pm in SR 318. All students and faculty are welcome to attend.

Ron Douglas

He earned his B.S. degree in from the Illinois Institute of Technology in 1960 and his Ph.D. from Louisiana State University in 1962. He has held academic positions at the University of Michigan, the State University of New York at Stony Brook, and Texas A&M University. Professor Douglas was Executive Vice President and Provost at Texas A&M from 1996-2002.

He has also held visiting positions at several universities throughout the world including Aarhus University, Australian National University, Szechuan University, Mittag-Leffler Institute, Tel Aviv University, the University of Newcastle upon Tyne, Bucknell University, and the Institute for Advanced Study at Princeton.

Ron Douglas has also been a Sloan Fellow and a Guggenheim Fellow. He was recently named a Fellow of the American Mathematical Society.

Title of Lecture: Complex Geometry and Operator Theory

At the end of the seventies, Mike Cowen and I showed that concepts and techniques from complex geometry could be used to study an important family of operators or commuting n-tuples of operators on complex Hilbert space. This family includes those arising as multiplication on Hilbert spaces of holomorphic functions such as the Hardy and Bergman spaces on the unit ball or polydisk. In this talk we will provide details on how a hermitian holomorphic bundle arises in these cases and how the Chern connection and curvature gives rise to unitary invariants for such operators. Moreover, we will demonstrate some applications in which the results are in the context of operator theory but the techniques come from complex geometry. Emphasis will be on familiar examples in the one variable case although the ideas and techniques apply more generally.