skip to content

Faculty of Mathematics

 

Career

  • 2002 Chair in Nonlinear Mathematical Science at the University of Cambridge, UK.
  • 1996 Chair in Applied Mathematics at Imperial College, UK.
  • 1986 Professor and Chairman of the Department of Mathematics and Computer Science of Clarkson University, USA.

Research

Thanasis Fokas current interests include:

  • Asymptotics of the Riemann zeta and related functions
  • Boundary value problems for linear and integrable nonlinear PDEs. 
  • Integrability in multi dimensions
  • Inverse Problems arising in Medicine, such as those arising in PET,SPECT, MEG and EEG
  • Novel techniques in complex analysis
  • Water waves

Selected of Publications

 

  •  A.S. Fokas and Y.C. Yortsos, On the Exactly Solvable Equation St = (βS + γ) -2Sxx +  α(βS + γ) -2Sx Occurring in Two-Phase Flow in Porous Media, SIAM J. Appl.Math. 42, 318-332 (1982).
  • A.S. Fokas and M.J. Ablowitz, On the Inverse Scattering Transform of Multi-Dimensional Nonlinear Equations Related to First Order Systems in the Plane, J. Math. Phys. 25, 2494-2505 (1984).
  • A.S. Fokas, Symmetries and Integrability, Stud. Appl. Math. 77, 253-299 (1987).
  • A.S. Fokas, J.B. Keller and B.D. Clarkson, Mathematical Models of Granulocypopoiesis and Chronic Myelogenous Leukemic, Cancer Res. 51, 2084-2091 (1991).
  • A.S. Fokas, A.R. Its and A.V. Kitaev, The Isomonodromy Approach to Matrix Models in 2D Quantum Gravity, Comm. Math. Phys. 147, 395-430 (1992).
  • A.S. Fokas and L.Y. Sung, On the Solvability of the N-Wave, the Davey-Stewartson and the Kadomtsev-Petviashvili Equation, Inverse Problems 8, 673-708 (1992).
  • A.S. Fokas and I.M. Gelfand, Surfaces on Lie Groups, on Lie Algebras, and their Integrability, Commun.  Math. Phys. 177, 203-220 (1996).
  • A.S. Fokas, A Unified Transform Method for Solving Linear and Certain Nonlinear PDE's, Proc. R. Soc. Lond. A 453, 1411-1443 (1997).
  • A.S. Fokas, Two Dimensional Linear PDE's in a Convex Polygon, Proc. R. Soc. Lond. A 457, 371-393 (2001).
  • A.S. Fokas, I.M. Gelfand and A.E. Kister, Prediction of the Structural Motifs of Sandwich Proteins, Proc. Natl. Acad. Sci. USA 101, 16780-16783 (2004).
  • A.S. Fokas and L.Y. Sung, Generalised Fourier Transforms, their Nonlinearisation and the Imaging of the Brain, Notices Amer. Math. Soc. 52, 1176-1190.
  • A.S. Fokas, A.R. Its and L.Y. Sung, The Nonlinear Schrödinger Equation on the Half-Line, Nonlinearity 18, 1771-1822 (2005).
  • M.J. Ablowitz, A.S. Fokas and Z.H. Musslimani, On a New Non-Local Formulation of Water Waves, J. Fluid. Mech., 562, 313-343 (2006).
  • A.S. Fokas, Electro-Magneto-Encephalography for the Three-Shell Model: Distributed Current in Arbitrary, Spherical and Ellipsoidal Geometries, J. R. Soc. Interface 6, 479-488 (2009).
  • A.S. Fokas and E.A. Spence, Synthesis as Opposed to Separation of Variables, SIAM Rev. 54, 291-324 (2012).
  • A.S. Fokas, O. Hauk and V.Michel, Electro-Magneto-Encephalography for the Three-Shell Model: Numerical Implementation for Distributed Current in Spherical Geometry, Inverse Problems 28, 035009 (2012).
  • A.S. Fokas and M.L. Glasser, The Laplace Equation in the Exterior of the Hankel Contour and Novel Identities for Hypergeometric Functions, Proc. R. Soc. Lond. A 469, 20130081 (2013).
  • G.A. Kastis, A. Gaitanis, A. Samartzis and A.S. Fokas, The SRT REconstruction Algorithm for Semiquantification in PET Imaging, Med. Phys. 42, 5970-5982 (2015).
  • A.S. Fokas, A.A. Himonas and D. Mantzavinos, The Nonlinear Schrödinger Equation on the Half-Line, Trans. Amer. Math. Soc. (in press).
  • A.S. Fokas and J. Lenells, On the Asymptotics to All Orders of the Riemann Zeta Function and of a Two-Parameter Generalization of the Riemann Zeta Function, Mem. Amer. Math. Soc. (submitted).

 

Publications

Relations among the Riemann zeta and Hurwitz zeta functions, as well as their products
ACL Ashton, AS Fokas
– Symmetry
(2019)
11,
754
An Adaptive Complex Collocation Method for Solving Linear Elliptic PDEs in Regular Convex Polygons Based on the Unified Transform
E-NG Grylonakis, CK Filelis-Papadopoulos, GAG null, AS Fokas
– Numerical Mathematics
(2019)
12,
348
A hybrid analytical-numerical algorithm for determining the neuronal current via EEG
P Hashemzadeh, AS Fokas, CB Schönlieb
(2019)
The Unified Transform: A Spectral Collocation Method for Acoustic Scattering
LJ Ayton, M Colbrook, A Fokas
– 25th AIAA Ceas Aeroacoustics Conference 2019
(2019)
An iterative spatial-stepping numerical method for linear elliptic PDEs using the Unified Transform
E-NG Grylonakis, CK Filelis-Papadopoulos, GA Gravvanis, AS Fokas
– Journal of Computational and Applied Mathematics
(2019)
352,
194
Correction to The unified transform for mixed boundary condition problems in unbounded domains
MJ Colbrook, LJ Ayton, AS Fokas
– Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
(2019)
475,
20190201
A hybrid analytical-numerical technique for elliptic PDEs
MJ Colbrook, TS Fokas, P Hashemzadeh
– SIAM J. Sci. Comput.
(2019)
41,
A1066
Ultra-relativistic gravity has properties associated with the strong force
AS Fokas
– The European Physical Journal C
(2019)
79,
271
A parallel unified transform solver based on domain decomposition for solving linear elliptic PDEs.
ENG Grylonakis, GA Gravvanis, CK Filelis-Papadopoulos, AS Fokas
– The Journal of Supercomputing
(2019)
75,
4947
The unified transform for mixed boundary condition problems in unbounded domains.
MJ Colbrook, LJ Ayton, AS Fokas
– Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences
(2019)
475,
20180605
  • <
  • 3 of 37
  • >

Research Groups

Cantab Capital Institute for the Mathematics of Information
Centre for Mathematical Imaging in Healthcare
Nonlinear Dynamical Systems

Room

F1.12

Telephone

01223 339733