Quantization proof of the uniform Yau-Tian-Donaldson conjecture



2023年9月25日:15: 30 — 18: 00

2023年9月26日:15: 30 — 18: 00

2023年9月27日:15: 30 — 18: 00


报告摘要:Searching for canonical metrics on a Kahler manifold is an important topic in geometric analysis. The canonical metrics we will be focusing on are twisted Kahler-Einstein metrics, whose existence is equivalent to the solvability of certain Monge-Ampere type equations. An important problem is to find suitable algebro-geometric conditions that can guarantee the solvability of such equations. This kind of problem is often referred to as the Yau-Tian-Donaldson conjecture. In this lecture series we will present a quantization approach, which shows the existence of twisted Kahler-Einstein metrics on any polarized manifolds provided that certain algebraic invariant (called the delta invariant) is bigger than one.