GENERAL
SEMINAR

“Algebraic
Geometric Techniques in Differential Geometry”

by

MUSTAFA
KALAFAT

METU

Abstract: Abstract: We will discuss how the tools from Algebraic
Geometry can be used to solve problems in Differential Geometry, and discuss
some of the relationships of these two fields. In particular, we will first
concentrate on the Self-Dual Metrics on 4-Manifolds. We prove that the
connected sum of two self-dual Riemannian 4-manifolds of positive scalar
curvature is again self-dual of positive scalar curvature, under a vanishing hypothesis.
The proof involves Kodaira-Spencer-Freedman
deformation theory and Leray Spectral Sequence. Later
on, if time permits we will discuss metrics on the Quotients of Enriques Surfaces, and applications of the Geometric Invariant
Theory, Complex/Almost Complex and Kahler structures.
At least the first half of the talk will be elementary and be accessible to the
general audience.

Date : November 23, 2011 (Wednesday)

Time : 15.40-16.30

Place: Bilkent University ,Mathematics Seminar Room SA141

Tea and cookies will be served before the seminar.