Yang Li received his PhD in 2019 from Imperial College London, under the guidance of Simon Donaldson and Mark Haskins. He has already made significant contributions to the understanding of Calabi-Yau metrics in complex differential geometry and Riemannian manifolds with exceptional holonomy. In a series of three papers, he studied the behaviour of Calabi-Yau metrics on 3-folds with holomorphic fibrations, when the fibres have small volume. He discovered a new complete Calabi-Yau metric on ℂ3 with singular tangent cone at infinity and showed that this gives a model for the behaviour around the critical points of the fibration, resolving an important question in the field.
In more recent work, he considers special Lagrangian fibrations, of the kind appearing in the Strominger-Yau-Zaslow picture of Mirror Symmetry, and obtained new models for the metric around singular fibres using a powerful combination of techniques from geometry and analysis. Yang's wider body of work includes many results on Yang-Mills connections, and the solution of the Plateau problem for maximal submanifolds.
Yang has been appointed as a Clay Research Fellow for a term of four years from 1 August 2020. He will be based at the Massachusetts Institute of Technology.
Photo: Mirko Mauri.