# 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

The attenuated spline reconstruction technique for single photon emission computed tomography.
NE Protonotarios, AS Fokas, K Kostarelos, GA Kastis
– Journal of the Royal Society Interface
(2018)
15,
20180509
Equations of motion of self-gravitating $N$-body systems in the first post-Minkowskian approximation
L Blanchet, AS Fokas
– Physical Review D
(2018)
98,
084005
Asymptotics to all orders of the Hurwitz zeta function
A Fernandez, AS Fokas
– Journal of Mathematical Analysis and Applications
(2018)
465,
423
Complexification and integrability in multidimensions
AS Fokas, MC Van der Weele
– Journal of Mathematical Physics
(2018)
59,
091413
Rogue waves of the nonlocal Davey–Stewartson I equation
J Rao, Y Zhang, AS Fokas, J He
– Nonlinearity
(2018)
31,
4090
Computing eigenvalues and eigenfunctions of the Laplacian for convex polygons
MJ Colbrook, AS Fokas
– Applied Numerical Mathematics
(2018)
126,
1
On the mass and thermodynamics of the Higgs boson
AS Fokas, CG Vayenas, DP Grigoriou
– Physica A Statistical Mechanics and its Applications
(2018)
492,
737
Uniform asymptotics as a stationary point approaches an endpoint
A Fernandez, EA Spence, AS Fokas
– IMA Journal of Applied Mathematics
(2018)
83,
204
EEG for Current With Two-Dimensional Support.
G Dassios, AS Fokas, P Hashemzadeh, RM Leahy
– IEEE Trans. Biomed. Engineering
(2018)
65,
2101
EEG for Current With Two-Dimensional Support
G Dassios, AS Fokas, P Hashemzadeh, RM Leahy
– IEEE transactions on bio-medical engineering
(2018)
65,
2101
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## Research Groups

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

F1.12

01223 339733