Dr Anthony Ashton
- 2013-2016: (October-) Stokes Fellow, Pembroke College, University of Cambridge.
- 2010-2013: (-October) Research Fellow, Emmanuel College, University of Cambridge.
- 2009-2010: EPSRC Prize Fellow, DAMTP.
- 2006-2009: PhD candidate, DAMTP.
- 2005-2006: Part III of Mathematics Tripos (CASM), University of Cambridge.
- 2002-2005: BA Mathematics, University of Cambridge.
Anthony is a member of the Department of Applied Mathematics and Theoretical Physics and works in the Applied and Computational Analysis group. He did his PhD under the supervision of Prof. A.S. Fokas. His research interests include: novel approaches to elliptic boundary value problems, Lie groups in PDEs, new approaches to rigorous problems in Linear PDE theory and certain aspects of mathematical physics.
He is lecturing the Part III course Distribution Theory & Applications, which focuses on classical distribution theory and application to the analysis of linear PDEs.
- Ashton & Crooks, 2013. Numerical study of the spectral Dirichlet-Neumann Map, in preparation.
- Ashton, 2013. Eigenvalues of the Laplacian on Convex Polygons - A New Approach, in preparation.
- Ashton & Fokas, 2012. Elliptic Boundary Value Problems in Convex Polygons with Distributional Boundary Data via the Unified Method. Submitted.
- Ashton, 2012. Inversion of a Symmetric Dirichlet-Neumann Map. Submitted.
- Ashton, 2012. The spectral Dirichlet-Neumann map for Laplace's equation in a convex polygon, SIAM J. Math. Analysis. To appear.
- Ashton, 2012. On the rigorous foundations of the Fokas method for linear elliptic PDEs, Proc. Roy. Soc. A 468(2142).
- Ashton & Fokas, 2011. A Nonlocal Formulation of Rotational Water Waves, J. Fluid. Mech. 689(1), 2011.
- Ashton, 2011. Regularity of Elliptic and Hypoelliptic Operators via the Global Relation, J. Part. Diff. Eq. 24(1).
- Ashton, 2011. On The Non-Existence of Three Dimensional Water Waves with Finite Energy, Nonlinear Analysis B 12(4).
- Ashton, 2010. Stability of Parallel Fluid Loaded Plates: A Nonlocal Approach, Stud. App. Math. 125(3).
- Ashton & Fokas, 2009. A Novel Approach to the Fluid Loaded Plate, Proc. Roy. Soc. A 465(2112).
- Ashton, 2008. Conservation Laws and Non-Lie Symmetries, J. Nonlin. Math. Phys. 15(3).
- Ashton, 2008. The Fundamential k-form and Global Relations, SIGMA 4(33).