MAT 644 
Topics in Differential Geometry 
Fall 2016 

TΘ 11:30-12:50
Physics P-125

Prof. Claude LeBrun.
Office: Math Tower 3-108.
Office hours: TΘ 2:00--3:30 pm.

Four-Manifolds, Einstein Metrics, and Differential Topology

This will be the first semester of a year-long course on the Riemannian geometry of smooth compact 4-manifolds. In general terms, we will discuss the interplay between a 4-manifold's differential topology and the curvature of the metrics it supports. Our main focus will be on Einstein metrics, with an emphasis on theorems about their existence or non-existence. We will also explore the corresponding uniqueness problem by studying moduli spaces of Einstein metrics on 4-manifolds.

The lectures will presuppose a basic knowledge of Riemannian geometry, roughly at the level of MAT 568. A familiarity with Kähler metrics, say at the level of MAT 545, could also be helpful.

Grades will be based upon class participation.

The Professor may be reach by e-mail by .
This is the best method for making appointments outside normal office hours.

Illustration: Smoothing of a Kummer surface with 16 real nodes. Graphic produced using the surf software package.

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