Andrew Zimmer, Fall 2020:
Math 823: Advanced Topics in Complex Analysis
Geometric problems in several complex variables
This class will consider geometric problems in several complex variables. At the beginning of the course we will introduce the Kobayashi, Bergman, and Kaehler-Einstein metrics on (certain) complex manifolds. Then rest of the class will be devoted to two topics:
(1) Consequences of negative curvature. The primary goal is to study the behavior of holomorphic functions on non-compact negatively curved Kaehler manifolds. References include: Yang (Duke Math. J. 1976), Yau (Amer. J. Math. 1978), Greene-Wu (Lecture Notes in Math. 1979), Wu-Yau (J. Amer. Math. Soc. 2020).
(2) Various notions of bounded geometry for complex manifolds. The primary goal is to describe work of Liu-Sun-Yau (J. Differ. Geom. 2004) on the geometry of Teichmuller spaces and later extensions of Yeung (Adv. Math. 2009).
The prerequisites of the class are a basic knowledge of one dimensional complex analysis and some differential geometry.
UW-Madison Department of Mathematics
Van Vleck Hall
480 Lincoln Drive
Madison, WI 53706