Let (X, D) be a polarized log variety with an effective holomorphic torus action, and Θ be a
closed positive torus invariant (1, 1)‐current. For any smooth positive function g defined on …

We construct a canonical Hausdorff complex analytic moduli space of Fano manifolds with
Kähler–Ricci solitons. This enlarges the moduli space of Fano manifolds with Kähler …

Let $(M, g, J, f) $ be an irreducible non-trivial K\"{a} hler gradient Ricci soliton of real
dimension $2 n $. We show that its group of isometries is of dimension at most $ n^ 2$ and …

This is largely an exposition article that expands the author's talk at the **amen International
Conference on Geometric Analysis in June 2021. We first survey the author's joint work with …

We find Fano threefolds $ X $ admitting K\" ahler-Ricci solitons (KRS) with non-trivial moduli,
which are $\mathbb {T} $-varieties of complexity two. More precisely, we show that the …

Let $(M, g, f, J,\lambda) $ be a complete K\"{a} hler gradient Ricci soliton. Our first theorem
classifies such a structure in real dimension four when $ f $ has a geodesic gradient, a …

This thesis contributes to the classification of log del Pezzo surfaces with torus action. Such
a surface is 1/k-log canonical if all discrepancies of a resolution of singularities are greater …

[Dedicated to Richard S. Hamilton on forty years of Ricci flow] Gradient Ricci solitons have
garnered significant attention both as self-similar solutions and singularity models of the …

In this paper, a growth estimate on the soliton potential is shown for a large class of
cohomogeneity one manifolds. This is used to construct continuous families of complete …

In this short note we determine the greatest lower bounds on Ricci curvature for all Fano T‐
manifolds of complexity one, generalizing the result of Chi Li. Our method of proof is based …