Xiuxiong Chen will deliver two distinguished lectures at ICMAT. Image courtesy of the researcher

Xiuxiong Chen (University of Science and Technology of China and Stony Brook University, USA) is the next speaker in the ICMAT Distinguished Lectures programme. He will give two talks focused on Kähler geometry on Friday 22 May, from 12:00 to 14:00, in the Aula Naranja at the Institute.

Chen, who turned out to be the last student of Eugenio Calabi (a central figure in the development of geometry in the second half of the last century), is internationally recognised for his contributions to complex differential geometry, Kähler geometry and partial differential equations. Particularly notable is his 2015 proof, together with his then student Song Sun and Fields medallist Simon Donaldson, of the conjecture on Fano manifolds. This conjecture, progressively developed between the late 1980s and the early 2000s by Shing-Tung Yau, Gang Tian and Simon Donaldson, stated that a K-stable Fano manifold admits a Kähler–Einstein metric. Their solution earned them the 2019 Oswald Veblen Prize in Geometry, one of the most important awards in geometry and topology, presented every three years.

In the first of his talks, entitled “On extremal metrics”, the researcher will offer a broad overview of constant scalar curvature Kähler metrics, an area in which he has worked throughout his career and which is currently one of the most active fields within differential geometry. Chen will discuss topics ranging from his doctoral thesis, in which he studied the existence of extremal Hermitian metrics on Riemannian surfaces, to Eugenio Calabi’s key works in the 1980s. He will also mention some of the most significant advances stemming from the so-called Donaldson programme in Kähler geometry and will focus on his recent work.

In his second lecture, “On extremal metrics with singularities”, Chen will analyse the extension of the Calabi–Donaldson theory in Kähler geometry to manifolds with cusp singularities (points on a curve where it ceases to be regular). He will discuss the existence and uniqueness of constant scalar flat Kähler metrics with cusp singularities and the study of lower bounds for the K-energy of the restricted Kähler class.

Xiuxiong Chen

Xiuxiong Chen is currently a professor at the University of Science and Technology of China (USTC), in the cities of Hefei and Shanghai, and at Stony Brook University (USA). He obtained his PhD in complex geometry and curvature in 1994 from the University of Pennsylvania, under the supervision of Eugenio Calabi.

In addition to the 2019 Oswald Veblen Prize in Geometry for his resolution of the conjecture on Fano manifolds, Chen was an invited speaker at the International Congress of Mathematicians (ICM) in Beijing in 2002. He was elected a fellow of the American Mathematical Society (AMS) in 2015 and a Simons fellow in mathematics in 2016. He has supervised more than 20 doctoral theses.

ICMAT Distinguished Lectures Programme

The ICMAT Distinguished Lectures feature leading figures in international mathematics. They provide a platform for sharing research topics of particular relevance to the mathematical community.

The programme began in 2021 with Fields medallist Charles Fefferman (Princeton University, USA, director of an ICMAT-Severo Ochoa Laboratory) and has since hosted mathematicians such as Claire Voisin (Institut de Mathématiques de Jussieu-Paris Rive Gauche, CNRS), Marie-Claude Arnaud (Université Paris-Cité), Jean-François Le Gall (Université Paris-Saclay), Yuri Tschinkel (New York University), Nigel Hitchin (University of Oxford), Thibault Damour (Institut des Hautes Études Scientifiques, Bures-sur-Yvette), Gilles Pisier (Sorbonne-Jussieu) and Ignacio Cirac (Max Planck Institute of Quantum Optics).