Our next meeting will be held in-person at UIC in room SEO636
Abstract: I will discuss the problem of understanding the long-time behavior of Ricci flow on a compact Kähler manifold, assuming that a solution exists for all positive time. Inspired by an analogy with the minimal model program in algebraic geometry, Song and Tian posed several conjectures which describe this behavior. I will report on joint work with Hein and Lee which confirms these conjectures.
Abstract: We prove that every (non-compact) Kähler-Ricci shrinker is naturally a polarized Fano fibration. The proof relies on Kähler reductions and Birkar’s boundedness result in birational geometry. Moreover, we propose several conjectures for Kähler-Ricci shrinkers, unifying the well-developed theories of Kähler-Einstein metrics and Calabi-Yau cones. This is joint work with Song Sun.