RTG Working Seminar

Wednesday, Sep. 10, 08	Liz Vivas (University of Michigan) Fatou Bieberbach Domain not intersecting two complex lines: It is an open question if there exists a biholomorphic map from $\mathbb{C}^2$ into $\{zw \neq 0\} \subset \mathbb{C}^2$. We will talk about what is known and potential techniques to solve this problem.
Wednesday, Sep. 24, 08	Chris Hammond (University of Michigan) Moving Frames and Normal Forms: We will discuss Cartan's and Chern's moving frames approach to the local equivalence problem for real hypersurfaces in C^n. We will also discuss recent work of Peter Olver relating normal forms to moving frames. If time allows, we will examine the relationship in a simple test case, e.g., real curves in two-dimensional real projective space.
Wednesday, Oct. 8, 08	Zhou Zhang (University of Michigan) Relative capacity and comparison principle: The goal is to give an elementary introduction of relative capacity and comparison principle introduced for the study of Monge-Amp\`ere operator. Their roles in Kolodziej's study of this operator will be illustrated. A little attention needs to be paid when considering manifolds instead of domains in complex spaces.
Wednesday, Nov. 5, 08	Michal Jasiczak (University of Poznan & Institute of Mathematics Polish Academy of Sciences) Division and interpolation on singular spaces: During this talk we intend to discuss the extension and division problem for holomorphic functions and differential forms near singularities of a complex space. We will apply desingularization argument and study the case of functions and forms that vanish to high order near the singular set.
Wednesday, Nov. 12, 08	Chris Hammond (University of Michigan) Complex Affinely Homogeneous Real Hypersurfaces in $C^{2}$: Abstract: Given a lie group G acting on a manifold M, one would like to classify all submanifolds L of a fixed dimension on which the action is transitive, e.g., what are the hypersurfaces for which the action is transitive. We will discuss a procedure developed by Doubrov, et al. for solving this problem. We will try to use it to find the real hypersurfaces in $C^{2}$ on which the group of complex affine trransformations acts transitively.
Wednesday, Nov. 19, 08	Elizabeth Wulcan (University of Michigan) The membership problem for polynomial ideals via residue currents: I will discuss how residue currents can be used to obtain effective versions of Hilbert's Nullstellensatz. The talk will be based on work by Andersson and Andersson-G\"otmark.
Monday, Dec. 8, 08 4-5pm, 3096 EH	Anna Siano (University of Michigan) Fatou-Bieberbach domains: A Fatou-Bieberbach domain is an open proper subset of $\C^n$ that is biholomorphic to $\C^n$. We will discuss examples of such domains that arise as basins of attraction of automorphisms of $\C^n$, following Rosay-Rudin's paper.