Tom Coates

Tom Coates is a Professor of Pure Mathematics in the Department of Mathematics at Imperial College London's Faculty of Natural Sciences. He holds affiliations with the Artificial Intelligence Network, the CNRS-Imperial Abraham de Moivre UMI, and the Pure Mathematics research group. His office is located in the Huxley Building (662) on the South Kensington Campus, London SW7 2AZ, and he can be contacted via email at t.coates@imperial.ac.uk or phone at +44 (0)207 594 3607.

Professor Coates' research spans pure mathematics with emphasis on algebraic geometry, mirror symmetry, and Gromov-Witten theory. He investigates quantum cohomology and Fano variety classification to construct a 'Periodic Table for shapes' through computational algebra, data mining, and machine learning. His work integrates geometric methods with cluster-scale computing to identify structural patterns in algebraic varieties, focusing on quantum periods, toric degenerations, and Laurent polynomial applications.

His recent publications (2021-2024) demonstrate a strong trend toward computational classification of Fano varieties and polytopes, leveraging machine learning for dimension prediction and database construction. Key themes include mirror symmetry via Laurent inversion, toric geometry applications, and connections between Gromov-Witten invariants and modular forms. These works often utilize custom tools like PCAS and Fanosearch for large-scale algebraic computations.

While specific student names are not listed, Professor Coates mentors PhD and Master's students in algebraic geometry and computational mathematics. His research is supported by the Simons Foundation, member institutions, and contributors, enabling international collaborations through networks like the CNRS-Imperial Abraham de Moivre UMI.

He leads a research team developing the Periodic Table for shapes framework, utilizing high-performance computing resources. The team maintains open-source tools including PCAS (Periodic Table for Algebraic Shapes) and Fanosearch for Fano variety exploration, with code repositories hosted on Bitbucket and quantum period databases published in Scientific Data.