March 6, 2008

Yanir Rubinstein (MIT/Princeton University)

Title: Quantizing harmonic maps into the space of Kahler metrics and Legendre duality of geometric flows

Abstract: The talk will be concerned with a problem of geometric quantization: How is the geometry of the infinite-dimensional space of Kahler metrics approximated in terms of the geometry of the finite-dimensional spaces of Fubini-Study Bergman metrics sitting inside it? We discuss recent joint work with S. Zelditch in which we prove that the harmonic map equation can always be solved and that such a map admits approximations by harmonic maps into the spaces of Bergman metrics on toric varieties. We also show a duality between the Eells-Sampson harmonic map flow and the heat flow under the Legendre transform.