Academic reports of Haitian scholars
Reporter: YANG Rongwei
Title: Hermitian geometry on resolvent set
Time: January 5,2023 AM 9:00-10:00
January 5, 2023AM 9:00-10:00
Location: A1101#room, Innovation Park Building
Contact: YANG Yixin (tel: 84708351-8135)
Abstract: Spectral theory is a central ingredient in operator theory. But it is ineffective on quasi-nilpotent operator (whose spectrum is the single point 0). In a joint work with R. Douglas, new Hermitian metrics are defined on the resolvent set, and it is shown that the set of blow up rates of the metrics at 0 is a good measure of V's lattice of hyper-invariant subspaces. In addition, some familiar objects, such as eigenvector or inner function, can be rediscovered by this metric.
The brief introduction to the reporter: YANG Rongwei is a Professor of Mathematics at State University of New York at Albany, USA. His research interests include: multi-variable operator theory, several vomplex variables, Hermitian bundles, Kahler geometry on Stein domains, Chern-Weil homomorphism, cyclic cohomology.
