**Department of Mathematics**

**COLLOQUIUM **

**"Einstein Equations from Geometric Viewpoint"**

By

# CANER KOCA

# (Vanderbilt
University)

** **

**Abstract: **The
Einstein Field Equations in General Relativity describe how the space-time must
be curved in the presence of matter and energy. These equations are of utmost
importance in mathematics as well: in vacuum, the solutions of these equations
are the metrics with "constant Ricci curvature", and thus, they give
a canonical preferred "shape" to the underlying manifold. In this
talk, I will give a survey of results on Einstein metrics, present lots of
examples (Calabi-Yau Manifolds, Gibbons-Hawking
Gravitational Instantons) and obstructions to their existence,
and indicate why these metrics are significant in the study of geometry.

**Date: ****Wednesday, April 22, 2015**

**Time: ****15.40-16.30**

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

** **

**All are most cordially invited.**

Tea and biscuits: after the seminar