Two ERC Advanced Grant Winners for WMI

Congratulations to Professor Tim Austin and Professor Felix Schulze, who have both been awarded ERC Advanced Grants. There were only 9 grants in Mathematics awarded overall, and only 3 in the UK.

ERC Advanced Grants are awarded to pioneering researchers with exceptional projects set to tackle key problems faced by the world. Of 56 Advanced Grants awarded to 24 UK institutions, academics at The University of Warwick have been awarded five unique projects.

Professor Tim Austin’s project - High-Dimensional Probability in Ergodic Theory and Representation Theory - will be looking at the interplay between two core fields of mathematics, graphs and groups, through a new lens.

A graph gives an abstract summary of the relationships between the objects in some collection. A group is an abstract collection of possible symmetries for other mathematical structures such as physical shapes. In both graph theory and group theory, rich veins of current research explore the asymptotic behaviours of sequences of these objects as they grow in 'size'.

Professor Austin’s work has recently uncovered a new analogy between these two fields. It depends on notions of 'entropy' that can be associated to such sequences. This ERC grant will support research into the resulting interplay between these two fields of mathematics. It will develop properties and applications of these notions and explore the ways in which results from one field can shed new light on the other as a result.

Professor Felix Schulze's Generic Regularity of Area Minimising Hypersurfaces & Mean Curvature Flows research program will be working to address an existing problem through a novel framework centred on generic regularity.

Picture a soap film spanning a loop of wire - it is in equilibrium since everywhere the surface tension forces are in complete balance. In mathematical terms this is known as a minimal surface and one can find ones that are in equilibrium but are not stable. There are arbitrary small perturbations that make them unbalanced rendering them close to impossible to witness as soap films. In higher dimensions, area minimising surfaces can exhibit singularities and it has been long been theorised that these singularities are what inherently make the configuration unstable, that is if they can be made to disappear by a suitable small perturbation.

Recent collaborations including Professor Schulze have already produced major advances, particularly in the context of area-minimizing hypersurfaces and mean curvature flows, demonstrating the profound potential of generic regularity to resolve long-standing open problems in geometric analysis.

The full list of Warwick awardees for 2025 can be found in this press releaseLink opens in a new window.