Course Description. This course will be a selected survey of recent topics in the area of (Riemannian) Einstein metrics, mainly concerned with existence and uniqueness questions. Many topics will not be touched on at all - for instance Kahler-Einstein metrics or relations with Seiberg-Witten theory; the latter has been covered well by Claude LeBrun in earlier years.

No text will be used for the course per se. Two useful general references for Einstein metrics are

• Einstein Manifolds, by A. Besse, Springer Verlag.
• Essays on Einstein Manifolds, Ed. C. LeBrun and M. Wang, Surveys in Differential Geometry, vol. 6, International Press.

A possible list of topics to be discussed includes:

• General survey and questions
• Structure of moduli spaces
• Gravitational instantons
• Classical aspects of the AdS/CFT correspondence, asymptotically hyperbolic Einstein metrics
• Glueing constructions and existence of Einstein metrics on "exotic" manifolds

Class Time and Place: Tu and Th 9:50 - 11:10 a.m., Physics, P-129.

Office Hours: MWF 1-2pm

Americans with Disability Act. If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disabled Student Services in ECC (Educational Communications Center) Building, Room 128, (631) 632-6748. They will determine with you what accomodations are necessary and appropriate. All information and documentation is confidential.
Students requiring emergency evacuation are encouraged to discuss their needs with their professors and Disabled Student Services. For procedures and information, go the following website: http://www.ehs.sunysb.edu/fire/disabilities/asp, here