Mathematics Department Colloquium: Integer points on affine cubic surfaces

Colloquium | April 11 | 4:10-5 p.m. | 60 Evans Hall

 Peter Sarnak, Princeton and IAS

 Department of Mathematics

A cubic polynomial equation in four or more variables tends to have many integer solutions, while one in two variables has a limited number of such solutions.There is a body of work establishing results along these lines. On the other hand very little is known in the critical case of three variables. For special such cubics, which we call Markoff type surfaces, a theory can be developed. We will review some of the tools used to deal with these and related problems. Joint works with A. Ghosh and with J. Bourgain and A. Gamburd.