CMSA Member Seminar

Speaker: Freid Tong (Harvard CMSA)

Title: On complete Calabi-Yau metrics and Monge-Ampere equations

Abstract: Calabi-Yau metrics are central objects in K\”ahler geometry and also string theory. The existence of Calabi-Yau metrics on compact manifolds was answered by Yau in his solution of the Calabi conjecture, but the situation in the non-compact setting is much more delicate, and many questions related to the existence and uniqueness of non-compact Calabi-Yau metrics remain unanswered. I will give an introduction to this subject and discuss some ongoing joint work with T. Collins and S.-T. Yau, on a new relationship between complete Calabi-Yau metrics and a new Monge-Ampere equation.