Our Spring 2026 meeting will be held in-person at Northwestern University (Harris Hall L07) on the 12th of May
Abstract: The Tian-Yau problem asks when a quasi-projective variety with trivial canonical bundle admits a complete Calabi-Yau metric. I will discuss some progress on this problem, and explain how it is related to the regularity theory for optimal transportation. Inspired by this connection, we obtain some new boundary regularity results for optimal transport.
Abstract: I will talk about a joint work with Minghao Miao, which proves that: in any dimension n, the second largest volume of Kahler-Einstein Fano manifolds is obtained exactly by the volume of quadric hypersurface and the product CP^1*CP^(n-1).
We prove this by using the theory of K-stability and its new connection with minimal rational curves on Fano manifolds. The singular case will also be discussed in its relation to the volume of Klt singularities.