Geometric analysis of analytic Toeplitz operators

题目:Geometric analysis of analytic Toeplitz operators

报告人:Professor Kunyu Guo,School of Mathematical Sciences,Fudan University

时间:2017年7月6日 10:00-11:00

地点:知新楼B座924

Abstract:This talk mainly focus on geometric analysis of symbol curves of analytic Toeplitz operators. Under a mild condition, we establish the connection between totally Abelian property and the Riemann surface defined by the symbol of analytic Toeplitz operator. it is found that winding numbers, indices and points of self-intersection of symbol curves of Toeplitz operator altogether play an important role in this topic.Techniques of algebraic topology, complex analysis, geometry, index theory and operator theory are intrinsic in our studies. As a byproduct, under a mild condition we provides an affirmative answer to a problem raised in [BDU,T1], and also construct some examples to show that the answer is negative if the associated conditions are weakened. This is a joint work with Hui Dan and Hansong Huang.