Anthony Charles Lewis Ashton

Dr. Anthony Charles Lewis Ashton is a Senior College Lecturer and Director of Studies at Homerton College, University of Cambridge, and a member of the Faculty of Mathematics. He works within the Department of Applied Mathematics and Theoretical Physics (DAMTP) in the Applied and Computational Analysis group. His academic career at Cambridge includes positions as Stokes Fellow at Pembroke College (2013-15) and Junior Research Fellow at Emmanuel College (2010-13).

• 2015-present: Senior College Lecturer and Director of Studies, Homerton College
• 2013-15: Stokes Fellow, Pembroke College
• 2010-13: Junior Research Fellow, Emmanuel College
• 2009-10: EPSRC Prize Fellow, DAMTP
• 2006-09: PhD Candidate, DAMTP
• 2005-06: Part III Mathematics, Peterhouse
• 2002-05: BA Mathematics, Peterhouse

Dr. Ashton's research focuses on novel approaches to elliptic boundary value problems, Lie groups in partial differential equations (PDEs), new approaches to rigorous problems in Linear PDE theory, and certain aspects of mathematical physics. His work demonstrates a consistent focus on developing innovative mathematical frameworks for solving complex PDE problems, particularly through the application of the unified Fokas method for boundary value problems.

His extensive publication record from 2007-2019 reveals a strong emphasis on elliptic PDEs, with particular attention to boundary value problems on convex domains. A significant portion of his work centers on the unified transform method (Fokas method), which provides a novel approach to solving boundary value problems for linear and integrable nonlinear PDEs. His research spans mathematical physics, fluid dynamics, and pure mathematical analysis, showing interdisciplinary connections between different areas of mathematics.

As an educator, Dr. Ashton has taught several advanced mathematics courses at Cambridge, including Part III Distribution Theory & Applications, Part II Integrable Systems, and Part IA Vector Calculus (2017-2020). His teaching materials demonstrate a commitment to making complex mathematical concepts accessible through well-structured handouts covering topics such as generating functions, Arnold-Liouville theorem, evolution of scattering data, and coordinate systems.