**DIFFERENTIAL
GEOMETRY SEMINAR**

**"Positively Curved
Einstein Metrics in Dimension 4"**

By

# CANER KOCA

# (Vanderbilt
University)

** **

**Abstract: **The
famous Frankel Conjecture in complex geometry, which was proved by Siu and Yau in the 1981, asserts
that the only compact complex n-manifold which admits a Kahler metric
of positive (bi)sectional curvature is
the complex projective n-space. In this talk, we prove this conjecture in complex dimension 2 under
weaker hypotheses: Namely, a compact
complex "surface", which admits a "conformally
Kahler" metric g of "positive
orthogonal holomorphic bisectional curvature" is
to the complex projective plane.

**Date: ****Tuesday, April
21, 2015**

**Time: ****10.40-11.30**

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

** **

** **

**All are most cordially invited.**

Tea and biscuits: after the seminar