Seminar on Complex Analysis and Complex Geometry - Spring 2017

Wednesday, February 8, 2017, 3-4pm, PGH 646A

Title: On geometry and dynamics of polynomial maps

Speaker: Yuefei Wang, Academy of Mathematics and Systems Science, Chinese Academy of Sciences

Abstract: We will talk about the global dynamics of Newton maps and geometry of polynomial maps and discuss problems and recent progress on complexity and critical singularities of polynomial maps.

Thursday, March 9, 2017, 3-4pm, room: AH 208

Title: Holomorphic isometries from the unit ball to bounded symmetric domains

Speaker: Yuan Yuan, Syracuse University

Abstract: I will first overview the classical holomorphic isometry problem between complex manifolds, in particular between bounded symmetric domains. When the source is the unit ball, in general the characterization of holomorphic isometries to bounded symmetric domains is not quite clear. With Shan Tai Chan, we recently characterize the holomorphic isometries from the unit disc to the product of the unit disc with the unit ball and obtained some interesting applications.

TUESDAY, March 21, 2017, 3-4pm, room: PGH 646A

Title: Value sharing of meromorphic functions, and functional equations

Speaker: Michael Zieve, University of Michigan

Abstract: Let p,q be nonconstant meromorphic functions on the complex plane. Nevanlinna showed that if p^{-1}(P_i)=q^{-1}(P_i) for five distinct points P_1,...,P_5 on the Riemann sphere, then p=q. I will present a generalization of this result to preimages of finite sets, however under the more restrictive hypothesis that the preimages are the same counting multiplicities. The result says that if there are five pairwise disjoint nonempty finite subsets S_1,...,S_5 of the Riemann sphere such that, for each i, the p- and q- preimages of S_i counted with multiplicities are identical to one another, then there is a nonconstant rational function f such that f o p = f o q. I will also explain recent work which come close to describing all solutions of this functional equation.

Thursday, March 30, 2017, 3-4pm, room: AH 7

Title: Kodaira dimension in geometry and topology

Speaker: Tian-Jun Li, University of Minnesota

Abstract: Kodaira dimension is a basic birational invariant of algebraic varieties, rooted from Kodaira's classification scheme of algebraic surfaces in the 50s. We will review various incarnations of Kodaira dimension in algebraic geometry, topology and symplectic geometry, and their cousin in differential geometry.