Andrew Zimmer, Fall 2020:

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.

credits:

3 credits

semester:

Fall

prereqs:

Math 722

UW_course_guide:

lastTaught:

Fall 2018