The Department of Mathematical Sciences will continue its free Math Seminar Series on Friday, November 16, at 10 a.m. in the Business and Science Building, Room 334. Two presentations will be given. The first is from Dr. John D’Angelo of the University of Illinois at Urbana-Champaign. Dr. D’Angelo will discuss, “Rational sphere maps.”
The abstract of Dr. D’Angelo’s talk is as follows:
I will begin with a short discussion of old results by many authors about rational sphere maps. I will then attempt to put these results into a general context. I will discuss work with Ming Xiao that associates various groups with proper holomorphic mappings. In the case of balls we proved that every finite subgroup of the source automorphism group arises as the Hermitian invariant group of a proper mapping between balls. I will discuss this result and some generalizations.
The second presentation, at 11:20 a.m., will be given by Friedrich Haslinger of the Universität Wien. Dr. Haslinger will present “The ∂-Neumann problem and Schrödinger operators.”
The abstract of Dr. Haslinger’s talk is as follows:
We apply methods from complex analysis, in particular the ∂-Neumann operator, to investigate spectral properties of Schrödinger operators with magnetic field (Pauli operators). For this purpose we consider the weighted ∂-complex on Cnwith a plurisubharmonic weight function. We derive a necessary condition for compactness of the corresponding ∂-Neumann operator (the inverse of the complex Laplacian) and a sufficient condition, both are not sharp. So far, a characterization can only be given in the complex 1-dimensional case.The Pauli operators appear at the beginning and at the end of the weighted ∂-complex. It is also of importance to know whether a related Bergman space of entire functions is of infinite dimension. In addition we consider the ∂-complex, where the underlying Hilbert space is the Fock space – the space of entire functions with the Gaussian weight.