**DIFFERENTIAL
GEOMETRY SEMINAR**

**"The Monge
–Ampere Equations and Yau's Proof of the Calabi Conjecture"**

By

# CANER KOCA

# (VANDERBILT UNIVERSITY)

** **

**Abstract: **The resolution of
Calabi's Conjecture by S.-T. Yau in 1977 is considered to be one of the
crowning achievements in mathematics in 20th century. Although the statement of
the conjecture is very geometric, Yau's proof involves solving a non-linear
second order elliptic PDE known as the complex Monge-Ampere equation.
An immediate consequence of the conjecture is the existence of Kähler-Einstein
metrics on compact Kähler manifolds with vanishing first Chern class (better
known as Calabi-Yau Manifolds).

In this expository talk, I will start with
the basic definitions and facts from geometry to understand the statement of
the conjecture, then I will show how to turn it into a PDE problem, and finally
I will highlight the important steps in Yau's proof.

**Date: ****Wednesday, May
21, 2014**

**Time: ****15:40 **

**Place: ****Mathematics Seminar Room,
SA-141**

** **

** **

**All are most cordially invited.**

Tea and biscuits: after the seminar