Events for 11/06/2009 from all calendars
Mathematical Physics and Harmonic Analysis Seminar
Time: 1:50PM - 2:40PM
Location: BLOC 627
Speaker: Constanze Liaw, Texas A&M
Title: Singular Integral Operators and Rank One Perturbations
Abstract: The spectral representation of a self-adjoint rank one perturbation is given by a singular integral operator of special form. Such operators are connected with two weight estimates for the Cauchy transform. As an application, a sufficient condition for the perturbed operator to have purely absolutely continuous spectrum on a closed interval is given in terms of the density of the unperturbed operator's spectral measure. (For those who have seen me speak about this topic previously, I am planning to emphasize regularizations of singular integral operators a little more. I'll give a somewhat related seminar on the same day in the linear analysis seminar -- see attached abstract.)
URL: Link
Algebra and Combinatorics Seminar
Time: 3:00PM - 3:50PM
Location: MILN 317
Speaker: Jon Kujawa, Oklahoma
Title: Varieties and Lie Superalgebras
Abstract: As we learned from Descartes, even if you are only interested in algebra questions, you can gain an awful lot of insight by looking at the related geometry. Following a long history in representations of finite groups and similar settings, I along with Boe and Nakano introduced varieties whose geometry tells you interesting things about the representation theory and combinatorics of Lie Superalgebras over the complex numbers. We will introduce these varieties and discuss some of our results and conjectures. The talk will start from scratch and should be accessible to grad students and non-specialists.
Geometry Seminar
Time: 4:00PM - 5:00PM
Location: MILN 216
Speaker: Christopher Manon, MSRI
Title: Phylogenetic algebraic geometry and the Verlinde formula
Abstract: Recent work of Sturmfels and Xu establishes an intriguing connection between the Hilbert functions of important projective varieties from phylogenetic algebraic geometry and a genus 0, sl_2(\C) case of the celebrated Verlinde formula from mathematical physics. We will discuss how this relationship can be constructed and generalized with the representation theory of affine Kac-Moody algebras and the associated theory of conformal blocks.
Linear Analysis Seminar
Time: 4:00PM - 5:00PM
Location: MILN 317
Speaker: Constanze Liaw, Texas A&M University
Title: Unitary rank one perturbations and the adjoint to the Clark operator
Abstract: Although the Clark operator was introduced over half a century ago, no complete representation formula has been published for its adjoint. However, partial representations have led to important results in Spectral Theory using Harmonic and Complex Analysis, and vice versa. Using vector-valued Functional Models, we derive a complete representation for the adjoint to the Clark operator.