### MATH 5031: Topics in Geometry and Topology II

**Description:** Advanced topics in geometry and topology. With a change of content this course is repeatable to a maximum of twelve credits.

**Credits:** 3

### MATH 5031 - Section 1: Topics in Complex Geometry

**Description:** We shall study Hodge theory, *L*^{2} estimates of the d-bar operator, and applications to Kodaira's vanishing and embedding theorems, and Calabi-Yau theorem. We shall also discuss hyperbolicity and positivity of the canonical bundle, including the Kobayashi and Lang conjectures. This course connects differential geometry to other fields. Through Hodge and *L*^{2} theory and Calabi-Yau theorem we develop tools of functional analysis, linear and nonlinear partial differential equations, and sheaf cohomology. When studying the Lefschetz decomposition we introduce the representation theory of the Lie algebra sl(2). We shall study Lang's conjecture which relates curvature and hyperbolicity to the problem of finiteness of rational points in number theory.

**Instructor:** Damin Wu

**Offered:** Spring

**Credits:** 3

**Sections: **Spring 2017 on Storrs Campus

PSCourseID | Course | Sec | Comp | Time | Room | Instructor |
---|---|---|---|---|---|---|

20441 | 5031 | 001 | Lecture | MWF 01:25:00 PM-02:15:00 PM | MONT101 | Wu, Damin |