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中科院华罗庚数学重点实验室

Some Topics in Several Complex Variables

Speaker：Prof. Genkai Zhang (University of Gothenburg)

Title：Weighed Bergman spaces on Siegel-Jacobi spaces:I. Reproducing kernels and analytic continuation, discrete spectrum of  Laplace operators;II. Bilinear-invariant differential operators.

Time：07.21,09:3011:30

Venue：N902

Abstract：In Part I, I'll study weighted Bergman spaces on the Siegel-Jacobi spaces and  their analytic continuation, finding the corresponding Wallach set. We prove that the  Jacobi-group invariant Laplace operator has positive eigenvalues above the zero eigenvalue (whose eigenspace is the weighted Bergman space). In Part II, I'll find a decomposition of tensor-products of the weighted Bergman spaces and the corresponding Rankin-Cohen brackets, generalizing my earlier work with Lizhong Peng.

SpeakerProf. Genkai Zhang (University of Gothenburg)

TitleTrace and Dixmier trace of curvature of infinite-dimensional vector bundles

Time07.22,09:3011:30

VenueN902

AbstractWe construct infinite dimensional vector bundle over the Siegel domain and over the Teichmüller space, and we compute the trace (Dixmier trace) of the curvature operator.