MAT 645 
Topics in Differential Geometry 
Spring 2023 

TΘ 1:15-2:35
Physics P-127

Prof. Claude LeBrun.
Office: Math Tower 3-108.
Office hours: TΘ 2:45-4:15 pm,
or by appointment.

Twistor Methods in Differential Geometry

This course will offer a self-contained introduction to twistor correspondences in Riemannian and pseudo-Riemannian geometry. Topics will include: self-dual 4-manifolds, self-dual Einstein metrics, hyper-Kähler manifolds, manifolds whose geodesics are all closed, and Einstein-Weyl geometry in dimension 3.

The course will presuppose a basic knowledge of Riemannian geometry, say on the level of MAT 568, Differential Geometry I. Some basic knowledge of complex manifolds, for example on the level of MAT 645, Complex Geometry, would also be extremely helpful.

Grades will be based upon attendance and class participation.

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

Illustration: Ruling lines on a quadric surface.

STUDENT ACCESSIBILITY SUPPORT SERVICES (SASC) STATEMENT: If you have a physical, psychological, medical, or learning disability that might impact your course work, please contact the Student Accessibility Support Center, Stony Brook Union Suite 107, at (631) 632-6748 or They will determine, with you, what accommodations are necessary and appropriate. All information and documentation will be treated as confidential.

ACADEMIC INTEGRITY STATEMENT: Students must pursue their academic goals honestly, and everyone must be personally accountable for all submitted work. Representing another person's work as your own is always wrong. The Academic Judiciary requires faculty members to report any suspected instances of academic dishonesty. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at

CRITICAL INCIDENT MANAGEMENT: Stony Brook University expects students to respect the rights, privileges, and property of other people. The Office of Judicial Affairs requires faculty members to report to any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.