Dr Anthony Ashton

 

Career

  • 2010-2013: Junior Research Fellow, Emmanuel College, University of Cambridge.
  • 2009-2010: Research 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.

Research

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 boundary value problems, Lie groups in PDEs, new approaches to rigorous problems in Linear PDE theory and certain aspects of mathematical physics.

Teaching

He is lecturing the Part III course Distribution Theory & Applications, which focuses on classical distribution theory and application to the analysis of linear PDEs.

Selected Publications

  • Ashton, Inversion of a Symmetric Dirichlet-Neumann Map, in preparation.
  • Ashton, Fourier Transforms of Surface Measures with Hölder Regularity, in preparation.
  • Ashton, Clifford Analysis and Boundary Value Problems, in preparation.
  • Ashton, Distributional Boundary Data for Elliptic Boundary Value Problems on Convex Polygons. in preparation.
  • Ashton & Fokas, On corner singularities for Elliptic Boundary Value Problems on Convex Polygons, In preparation.
  • Ashton, On the rigorous foundations of the Fokas method for linear elliptic PDEs, Proc. Roy. Soc. A (to appear).
  • Ashton & Fokas, A Nonlocal Formulation of  Rotational Water Waves, J. Fluid. Mech. 689(1), 2011.
  • Ashton, Regularity of Elliptic and Hypoelliptic Operators via the Global Relation, J. Part. Diff. Eq. 24(1), 2011.
  • Ashton, On The Non-Existence of Three Dimensional Water Waves with Finite Energy, Nonlinear Analysis B 12(4), 2011.
  • Ashton, Stability of Parallel Fluid Loaded Plates: A Nonlocal Approach, Stud. App. Math. 125(3), 2010.
  • Ashton & Fokas, A Novel Approach to the Fluid Loaded Plate, Proc. Roy. Soc. A 465(2112), 2009.
  • Ashton, Conservation Laws and Non-Lie Symmetries, J. Nonlin. Math. Phys. 15(3), 2008.
  • Ashton, The Fundamential k-form and Global Relations, SIGMA 4(33), 2008.