MAT 683 
Advanced Topics in
Differential Geometry 
Spring 2017 

TΘ 2:30-3:50
Physics P-125

Prof. Claude LeBrun.
Office: Math Tower 3-108.
Office hours: TΘ 11:00 am--12:30 pm.

Four-Manifolds, Einstein Metrics, and Differential Topology II

This will be the second semester of a year-long course on the Riemannian geometry of smooth compact 4-manifolds. Much of the course will focus on the way that Seiberg-Witten invariants reveal an 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 knowledge of the material we covered in MAT 644 last semester. A familiarity with Kähler metrics, say at the level of MAT 545, could also be particularly 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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