Title: Product Theorem via semidefinite programming
Speaker: Rajat Mittal, Rutgers University
Date: Wednesday, March 5, 2008 11:00-12:00pm
Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ
The tendency of semidefinite programs to compose perfectly under product has been exploited many times in complexity theory: for example, by Lovasz to determine the Shannon capacity of the pentagon; to show a direct sum theorem for non-deterministic communication complexity and direct product theorems for discrepancy; and in interactive proof systems to show parallel repetition theorems for restricted classes of games.
Despite all these examples of product theorems---some going back nearly thirty years---it was only recently that Mittal and Szegedy began to develop a general theory to explain when and why semidefinite programs behave perfectly under product. This theory captured many examples in the literature, but there were also some notable exceptions which it could not explain---namely, an early parallel repetition result of Feige and Lovasz, and a direct product theorem for the discrepancy method of communication complexity by Lee, Shraibman, and Spalek. In this talk we explain these cases.
Joint work with Troy Lee.