Noncommutative Geometry Seminar

Date: December 2, 2015

Time: 2:00PM - 2:50PM

Location: BLOC 628

Speaker: Yi Wang, Texas A&M University

Title: Geometric Arveson-Douglas Conjecture and Holomorphic Extension

Abstract: We introduce techniques from complex harmonic analysis to prove a weaker version of the Geometric Arveson-Douglas Conjecture for complex analytic subsets that is smooth on the boundary of the unit ball and intersects transversally with it. In fact, we prove that the projection operator onto the corresponding submodule is in the Toeplitz algebra, which implies the essential normality of the submodule. We use this to prove that for a radical polynomial ideal I whose zero variety satisfies the above condition, it’s closure is essentially normal as a Hilbert module. A key technique is defining a right inverse operator of the restriction map from the unit ball to the analytic subset generalizing the result in holomorphic extension theory.