Seminar on Complex Analysis and Complex Geometry - Fall 2009

           All talks in 646A PGH, Wednesday, 11:00-12:00 AM

           Wednesday, September 9, 2009

Title: On questions related to definite curvature in algebraic geometry, I
Speaker: Dr. Gordon Heier, University of Houston
Abstract: The object of these talks is to give an accessible presentation of a body of work in algebraic geometry centered around the notion of definite curvature. We will start with the basics of (complex) algebraic geometry, such as projective varieties, line bundles and metrics and show the path to modern techniques, theorems and open problems, mostly relating to the Fujita Conjecture and Kaehler-Einstein metrics.These talks will not be technical, and hopefully give -- especially young members of the department -- a glimpse of exciting research areas that are being studied in universities and institutes around the world.

          Wednesday, September 16, 2009 

          Title: On questions related to definite curvature in algebraic geometry, II

Speaker: Dr. Gordon Heier, University of Houston
Abstract: See above

           Wednesday, September 23, 2009

Title: On the Second Main Theorem and its applicaiton in the study of the uniqueness problem, I
Speaker: Dr. Min Ru, University of Houston
Abstract: In this series of talks (proposed two talks), I'll discuss how to use the theory of Carlson and Griffiths, as well as the recent result of Demailly on the partial solution to the Fujita's conjecture to obtain some uniqueness results on equi-dimensional meromorphic mappings. I also will discuss the use of the recent SMT obtained by myself in the study of the uniqueness problems.

          Wednesday, October 7, 2009

          Wednesday, October 14, 2009

          Wednesday, October 28, 2009

Title: Gauss-Bonnet theorem on moduli spaces
Speaker: Dr. Zhiqin Lu
Abstract: In this talk, I show the proof  the Gauss-Bonnet-Chern theorem on moduli space of polarized Kahler manifolds. Using the results, I show the proof the rationality of the Chern-Weil forms (with respect to the Weil-Petersson metric) on CY moduli. As an application in physics, by the Ashok-Douglas theory, counting the number of flux compactifications of the type IIb string on a Calabi-Yau threefold is related to the integrations of various Chern-Weil forms. I will show that all these integrals are finite (and also rational). This is joint with Michael R. Douglas.

Wednesday, November 11, 2009
 
Title: Regularity in the dbar-Neumann problem: open questions
Speaker: Dr. Emil Straube
Abstract: I will discuss several questions related to various regularity properties of the dbar-Neumann operator. These questions include existence of "good" plurisubharmonic functions, presence or absence of discs in the boundary
(more generally, of sets that "pick up plurisubharmonic hull"), vanishing of a certain cohomology class, and existence of Stein neighborhood bases for the closure of the domain.

Wednesday, November 18, 2009

Title: Closed symmetric differentials of degree 2 and the topology of complex surfaces
Speaker: Dr. Bruno De Oliveira - University of Miami
Abstract: This talk has as general theme the pursuit of a holomorphic theory of the fundamental group. Symmetric differentials on a complex manifold in general do not encode topological information about the manifold. We characterized globally a class of symmetric differentials which we call closed and then provide their complete local description. Next we determine what is the topological data about the manifold that is reflected on closed symmetric differentials of degree 2. In particular, we shall demonstrate that the presence of a closed symmetric differential of degree two on a complex surface X implies that either the fundamental group of X is infinite or that there is an exceptional locus E such that the complement X\E has an infinite fundamental group.