We prove the existence of a Kähler–Einstein metric on a K–stable Fano manifold using the
recent compactness result on Kähler–Ricci flows. The key ingredient is an algebrogeometric …

We develop a compactness theory for super Ricci flows, which lays the foundations for the
partial regularity theory in Bamler (Structure Theory of Non-collapsed Limits of Ricci Flows …

In this paper we characterize non-collapsed limits of Ricci flows. We show that such limits
are smooth away from a set of codimension $\geq 4$ in the parabolic sense and that the …

We show that a polarized affine variety with an isolated singularity admits a Ricci flat Kähler
cone metric if and only if it is K–stable. This generalizes the Chen–Donaldson–Sun solution …

We prove an algebraic version of the Hamilton–Tian conjecture for all log Fano pairs. More
precisely, we show that any log Fano pair admits a canonical two-step degeneration to a …

In this paper we analyze Ricci flows on which the scalar curvature is globally or locally
bounded from above by a uniform or time-dependent constant. On such Ricci flows we …

The metaverse concept constructs a virtual world parallel to the real world. The social
economic dynamics (SED) model establishes a systematic model for social economic …

We prove that for any $\mathbb {Q} $-Fano variety $ X $, the special $\mathbb {R} $-test
configuration that minimizes the $ H $-functional is unique and has a K-semistable $\mathbb …

We prove that on Fano manifolds, the Kähler–Ricci flow produces a “most destabilising”
degeneration, with respect to a new stability notion related to the $ H $-functional. This …

These lecture notes provide an introduction to the study of the Kähler–Ricci flow on compact
Kähler manifolds, and a detailed exposition of some recent developments. RÉSUMÉ.— Ces …