Seminar on Complex Analysis and Complex Geometry - Spring 2011

Wednesday, January 26, 2011, 12noon, PGH 348

Title: Towards a dynamical Manin--Mumford conjecture.

Speaker: Shouwu Zhang, Columbia University

Abstract: We provide a family of counterexamples to a first formulation of the dynamical Manin-Mumford conjecture. We propose several revisions of this conjecture and some evidences.

Wednesday, January 26, 2011, 3pm, SEC 202 (Colloquium)

Title: Calabi-Yau Theorem and algebraic dynamics.

Speaker: Shouwu Zhang, Columbia University

Abstract: We prove the uniqueness part of the Calabi-Yau theorem for metrized line bundles over non-archimedean analytic spaces, and apply it to endomorphisms with the same polarization and the same set of preperiodic points over a complex projective variety.

Wednesday, February 2, 2011, 12noon, PGH 348

Title: Working Seminar

Speaker: Gordon Heier, UH

Wednesday, February 9, 2011, 12noon, PGH 348

Title: Working Seminar

Speaker: Gordon Heier, UH

Wednesday, February 16, 2011, 12noon, PGH 348

Title: Working Seminar

Speaker: Min Ru, UH

Wednesday, February 23, 2011, 12noon, PGH 348

Title: Working Seminar

Speaker: Gordon Heier, UH

Wednesday, March 2, 2011, 12noon, PGH 348

Title: Working Seminar

Speaker: Gordon Heier, UH

Wednesday, March 9, 2011, 12noon, PGH 348

Title: Working Seminar

Speaker: Gordon Heier, UH

Wednesday, March 23, 2011, 12noon in PGH 348

Title: Indices and Relative Indices in CR-geometry

Speaker: Charles Epstein, University of Pennsylvania

Abstract: It is well known that most CR-structures on strictly pseudoconvex 3d-CR manifolds cannot be obtained as the boundary of a Stein space. We discuss an approach to studying the set of embeddable perturbations of an embeddable structure that uses a global invariant, called the relative index. We explain how to define and compute this index and its application to show that the set of embeddable perturbations is closed in certain cases.

Wednesday, March 23, 2011, 3:00pm, UH Hilton Shamrock Room (Colloquium)

Title: A new method for the numerical solution of Maxwell's equations

Speaker: Charles Epstein, University of Pennsylvania

Abstract: I will discuss recent joint work with Leslie Greengard on a new representation of solutions to the time harmonic Maxwell Equations. Using this representation we reduce the solution of the classical problems of scattering off of a smooth bounded interface to the solution of Fredholm integral equations of second kind on the interface. What distinguishes our representation is that it does not have any spurious "interior" resonances, or suffer from low frequency breakdown. It also reveals some interesting topological features of the time harmonic equations at non-zero frequencies.