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He is a rare example of a scientist in the style of renaissance
Israil Moiseevic Gelfand about A.S. Fokas

Athanassios (Thanasis) Spyridon Fokas (Θανάσης Σπυρίδων Φωκάς) was born in Argostoli (Kefalonia), Greece. He obtained a BSc in Aeronautics from Imperial College (1975), a PhD in Applied Mathematics from the California Institute of Technology (1979) and an MD from the University of Miami, School of Medicine (1986).
His remarkably broad education in engineering, mathematics and medicine, combined with his exceptionally high analytical technique and deep intuition, allowed him to make fundamental contributions to both theory and applications.

He is renowned in the area of nonlinear integrable equations. A method for solving initial value problems for integrable nonlinear evolution equations PDEs in one space dimension was developed in the late sixties through the pioneering work of Kruskal and Lax. However, the problem of developing a method for solving integrable nonlinear evolution PDEs in two dimensions remained open until the early eighties, when Fokas and Ablowitz developed the so called d-bar method.

The above works were about initial-value problems. Boundary value problems which are more difficult to solve (but also physically more important) were finally solved by Fokas after twenty years of hard work. For this work and in particular for his "unified transform method", which has been recognized as one of the most important developments in the analysis of differential equations since the work of the classics of the eighteenth century, he was awarded the Naylor Prize of the London Mathematical Society in 2000. He has also been instrumental in the solution of two long standing crucial, open problems in brain imaging, namely the solution of the basic mathematical problems characterizing magnetoencephalography as well as single photon emission computerised tomography.

Awards

A. S. Fokas, received the 2000 NAYLOR PRIZE for mathematics of the London Mathematical Society ( the most recognised prize for applied mathematics, awarded by the British Mathematics Society). Professor Fokas is the first non-British scientist to be so honoured. (actually, it was for his work in areas other than just linear equations that he received the prize - for details see http://www.lms.ac.uk/activities/prizes_com/citations00/fokas.html ).Some of the previous recipients of the Naylor prize are: Michael V Berry, S. W. Hawking, Roger Penrose and others important mathematicians and physicists.
In 2002 he was appointed to the newly inaugurated chair in Nonlinear Mathematical Science at the University of Cambridge.
In 2004 he was awarded the ARISTEION PRIZE of the Academy of Athens (the most prestigious prize of the Academy given every four years to a single scholar chosen from science, engineering, or medicine). He was elected a full member of the Academy of Athens (the Academy considers itself the continuation of the Academy of Plato and has about 45 members covering all areas including sciences, engineering, medicine, arts, letters, political and moral sciences; A.S. Fokas, who is the youngest member of the Academy, is the sixth mathematician elected in the Academy - the first was C. Caratheodory - and the first ever applied mathematician).
In 2004 he was awarded an Honorary Doctorate of Sciences from the Technical University of Crete.
Honorary member of the Institute of Computational and Applied Mathematics, Greece.
In January 2005 he was presented with the decoration of the Commander of the Order of Phoenix by the President of the Hellenic Republic

Professional Activities

Member of the International Advisory Board of the Institute of Mathematical Sciences, Imperial College, UK.
Member of the Advisory Board of the Centre for Nonlinear Mathematics and Applications , Loughborough University, UK
Co-Editor in chief of the Journal of Nonlinear Science
Associated Editor of the Series: Progress in Physics and Mathematical Physics (Birkhäuser)
Member of the Editorial Board of the following Journals:
- Proceedings of the Royal Society (Series A)
- Selecta Mathematica
- Journal of Mathematical Physics
- Studies in Applied Mathematics
- Mathematical Physics, Analysis and Geometry
- The Quarterly Journal of Mechanics and Applied Mathematics
- Journal of Mathematical Analysis and Applications
- Abstract and Applied Analysis
- Journal of Nonlinear Mathematical Physics
- Bulletin of the Greek Mathematical Society
- Communications in Applied Analysis
- International Journal of Differential Equations and Applications
- International Mathematical Journal
- International Journal for Rapid Publications in Mathematics

Books

M J Ablowitz and A S Fokas, Introduction and Applications of Complex Variables, Cambridge Univ. Press, second edition (2003)
A S Fokas, A R Its , A A Kapaev and V Yu Novokshenov , Painlevé Transcendents as Nonlinear Special Functions, AMS (in press)

Co-Editor

A S Fokas and V E Zakharov , Eds. Important Developments in Soliton Theory, Springer-Verlag (1993)
A S Fokas, D J Kaup , A C Newell and V E Zakharov, Eds. Nonlinear Processes in Physics, Springer-Verlag (1993)
A S Fokas and I M Gelfand , Eds. Algebraic Aspects of Integrable Equations, Birkhauser (1996)
A S Fokas, A Grigorian, T Kibble and B Zegarlinsky, Eds. Mathematical Physics 2000, Imperial College Press (2000)
A S Fokas, A Grigorian, T Kibble and B Zegarlinsky, Eds. XIII International Congress of Mathematical Physics, International Press (2002)
A. Fokas, J. Halliwell, T. Kibble, B. Zegarlinski, Eds. Highlights of Mathematical Physics, AMS (2002).

Co-editor of the special issue Integrability, Topological Solitons and Beyond, A.S. Fokas, N.S. Manton, R.G. Newton, Eds. Journal of Mathematical Physics, Vol. 44 (2003).

Selected Publications

Fokas is the author of more than 200 papers in such diverse areas as models for leukaemia (with J B Keller), singular perturbation (with P Lägerstrom), magnetoencephalography (with Y Kurylev and I M Gelfand), bi-Hamiltonian structures (with B Fuchssteiner and I M Gelfand), nonlinear singular integro-differential equations (with M J Ablowitz and M D Kruskal), Painleve equations (with X Zhou), orthogonal polynomials-quantum gravity (with A R Its) and nonlinear multidimensional PDEs (with R R Coifman and L Y Sung). He is internationally recognised in the field of nonlinear integrable equations. In the Special Millenium Issue: Mathematical Physics - Past and Future of the Journal of Mathematical Physics, June 2000, which summarised the "most important developments in mathematical physics in the 20th century", Fokas was asked to contribute an article on integrability.

Boundary Value Problems for Linear and Integrable Nonlinear Two-Dimensional PDEs

A.S. Fokas and B. Pelloni, Integral Transforms, Spectral Representation and the d-bar Problem, Proc. R. Soc. Lond. A 456, 805-833 (2000).
A.S. Fokas, Two dimensional linear PDEs in a convex polygon, Proc. R. Soc. A, 457, 371-393 (2001)
D. ben-Avraham and A.S. Fokas, The Modified Helmholtz Equation in a Triangular Domain and an Application to Diffusion-limited Coalescence, Phys. Rev. E 64, 016114-6 (2001).
A.S. Fokas, A new transform method for evolution PDEs, IMA J. Appl. Math. 67, 559 (2002)
A.S. Fokas, Integrable Nonlinear Evolution Equations on the Half-Line, Comm. Math. Phys. 230, 1-39 (2002).
A.S. Fokas and P.F. Schultz, The long-time asymptotics of moving boundary problems using an Ehrenpreis-type representation and its Riemann-Hilbert nonlinearisation, Communications of Pure and Applied Maths, 1-40 (2002).
A.S. Fokas, Linearizable initial boundary value problems for the sine-Gordon equation on the half-line, Nonlinearity 17, 1521-1534 (2004).
A.S. Fokas and A.R. Its, The nonlinear Schrodinger equation on the interval, J. Phys. A: Math Gen. 37, 6091-6114 (2004).
A.S. Fokas, Boundary-value problems for linear PDEs with variable coefficients, Proc. R. Soc. Lond. A 460, 1131-1151 (2004).
D. Crowdy and A.S. Fokas, Explicit Integral Solutions for the Plane Elastostatic Semi-Strip, Proc. R. Soc. Lond. 460, 1285-1309 (2004).
A.S. Fokas and S. Kamvissis, Zero dispersion limit for integrable equations on the half-line with linearisable data, Abstract and Applied Analysis 5, 361-370 (2004).
Y.A. Antipov and A.S. Fokas, A transform method for the modified Helmholtz equation in a semi-strip, Math. Proc. Camb. Phil. Soc. (in press).
A.S. Fokas and B. Pelloni, A transform method for evolution PDEs on the interval, IMA J. Appl. Math. (in press).
G. Dassios and A.S. Fokas, The basic elliptic equation in an equilateral triangle (preprint).

Multidimensional Nonlinear Integrable PDEs

A.S. Fokas and A.K. Pogrebkov, Inverse scattering transform for the KPI equation on the background of a one-line soliton, Nonlinearity, 16, 771-783 (2003).
A.S. Fokas, The Davey-Stewartson I equation on the quarter plane with homogeneous Dirichlet boundary conditions, J. Math. Phys. 4, 3226-3244 (2003).
M. McConnell, A.S. Fokas and B. Pelloni, Localised coherent structures of the DSI and DSII equations - A numerical study (preprint).

Fluid Mechanics

J.D. Gibbon, A.S. Fokas and C.R. Doering, Dynamically streched vortices as solutions of the Navier-Stokes equations, Physica D 132, 497-510 (1999).
A.S. Fokas, Steady inviscid hydrodynamics with constant speed (preprint).
A.S. Fokas and D.T. Papageorgiou, Absolute and convective instability for evolution PDEs on the half-line (preprint).
M.J. Ablowitz and A.S. Fokas, A new formulation of three-dimensional water waves (in preparation).

Medical Imaging

A.S. Fokas, Applied Mathematics and the Imaging of the Brain, Bull. Greek Math. Soc. 47, 3-18 (2003)
A.S. Fokas, Y. Kurylev and V. Marinakis, On the unique determination of neuronal currents in the brain via magnetoencephalography, Inverse Problems 20, 1067-1082 (2004).
A.S. Fokas and V. Marinakis, A Numerical Reconstruction Algorithm for Positron Emission Tomography and Single Photon Emission Computed Tomography (preprint).