We prove the following result: if a\,\,\,\, Q\,\,\,\,\, Q-Fano variety is uniformly K-stable, then it
admits a Kähler–Einstein metric. This proves the uniform version of Yau–Tian–Donaldson …

We formulate a notion of K-stability for K\" ahler manifolds, and prove one direction of the
Yau-Tian-Donaldson conjecture in this setting. More precisely, we prove that the Mabuchi …

We establish a uniform Sobolev inequality for K\" ahler metrics, which only require an
entropy bound and no lower bound on the Ricci curvature. We further extend our Sobolev …

We prove the Yau‐Tian‐Donaldson conjecture for any ℚ‐Fano variety that has a log smooth
resolution of singularities such that a negative linear combination of exceptional divisors is …

We prove a uniform diameter estimate and a uniform local non-collapsing of volumes for a
large family of Kaehler metrics generalizing those obtained recently by Guo-Phong-Song …

We study asymptotic distribution of zeros of random holomorphic sections of high powers of
positive line bundles defined over projective homogenous manifolds. We work with a wide …

The space of Kähler metrics, on the one hand, can be approximated by subspaces of
algebraic metrics, while, on the other hand, it can also be enlarged to finite‐energy spaces …

In this work we prove a universality result regarding the equidistribution of zeros of random
holomorphic sections associated to a sequence of singular Hermitian holomorphic line …

We study the existence of extremal Kähler metrics on Kähler manifolds. After introducing a
notion of relative K-stability for Kähler manifolds, we prove that Kähler manifolds admitting …

We survey results on the distribution of zeros of random polynomials and of random
holomorphic sections of line bundles, especially for large classes of probability measures on …