MAT 644 
Topics in Differential Geometry 
Fall 2012 

TΘ 11:30-12:50
Physics P-124

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

The Curvature of Four-Manifolds

This will be the first semester of a year-long course on the Riemannian geometry of smooth compact 4-manifolds. Our main objective will be to understand how the differential topology of a 4-manifold constrains the curvature of the Riemannian metrics it supports. We will be particularly interested in the geometrization of 4-manifolds by metrics such as Einstein metrics and self-dual metrics, and one of the main goals of the course will be to outline the proofs of a number of existence and non-existence results regarding these special Riemannian metrics.

The lectures will presuppose a basic, core knowledge of Riemannian geometry, roughly at the level of MAT 568. Some familiarity with Kähler metrics, say at the level of MAT 545, would 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: Kummer surface with 16 real nodes. Graphic produced using surf software package.

DSS advisory. If you have a physical, psychiatric, medical, or learning disability that could adversely affect your ability to carry out assigned course work, please contact the Disabled Student Services office (DSS), Educational Communications Center (ECC) Building, room 128, (631) 632-6748.  DSS will review your situation and determine, with you, what accommodations are necessary and appropriate. All information and documentation regarding disabilities will be treated as strictly confidential.

Students for whom special evacuation procedures might be necessary in the event of an emergency are encouraged to discuss their needs with both the instructor and with DSS. Important information regarding these issues can also be found at the following web site: