Geometric Analysis and Topology Seminar

---

A YTD correspondence for constant scalar curvature metrics

Speaker: Tamas Darvas, University of Maryland

Location: Warren Weaver Hall 512

Date: Friday, May 1, 2026, 11 a.m.

Synopsis:

We provide a uniform Yau–Tian–Donaldson correspondence characterizing the existence and uniqueness of constant scalar curvature Kähler metrics on compact Kähler manifolds. Our approach introduces a family of energy functionals, analogous to the Ding energy in the Fano case, via Berman’s transcendental quantization. We compute their slopes along test configurations using intersection theory. Combining these methods with the non-Archimedean framework of Sébastien Boucksom and Mattias Jonsson, we show that coercivity of the Mabuchi energy can be tested on a distinguished class of Chi Li–type log discrepancy models, thus yielding another uniform Yau–Tian–Donaldson correspondence (joint with Kewei Zhang).