Athanassios Fokas #

Integrable systems: since his involvement in this area in the early 1980s, together with collaborators have solves all the major open problems in the main area of integrable systems , namely, in integrable evolution equations.

Painleve equations, orthogonal polynomials and random matrices: the work of Fokas-Its-Kitaev led to the reformulation of orthogonal polynomials in terms of the Riemann -Hilbert formalism, which revived this classical area of mathematics.

Boundary value problems of linear and integrable nonlinear PDEs: he introduced a completely new method, refereed by hundreds of researches as the 'Fokas method' which has had a tremendous impact in the theory of boundary value problems.

Functional medical imaging: in the early 1990s, jointly with Israel Gelfand they introduced a new, powerful approach for inverting integrals. This method,was used 10 years letter by Roman Novikov for the inversion of the attenuated Radon transform which provides the mathematical basis of the important imaging technique of Single Photon Emission Computerized Tomography(SPECT). Fokas is the director of the Mathematics Centre of the Academy of Athens, where the above formula has been simplified and implemented numerically (as well as the analogous formula for Positron Emission Tomography).

Electro-magneto-enchephalography: in the early 1990s Fokas and Gelfand began the investigation of a problem that had remained open since the seminal investigations of Helmholtz, namely to determine which part of the current in a conductor can be determined from the knowledge of the magnetic flux measured outside the conductor. This problem for a realistic brain-head model was finally solved by Fokas in 2009.

Asymptotic Analysis: in a recent paper published in the Memoirse of the AMS, Fokas and Lenells computed the asymptotics of the Riemann zeta function to all orders. Furthermore, Fokas has introduced a completely new approach towards the Lindelof hypothesis based on the introduction and asymptotic analysis of a novel integral equation satisfied by the Riemann zeta function. In a different development, Blanchet , a world expert on the post-Newtonia approximation of the 2-body problem in the General Theory of Relativity, and Fokas have computed the first post- Minkowskian approximation of the N-body problem in the General Theory of Relativity.

Applications in medicine and biology: together with J.B. Keller they have presented and solved mathematical models for chronic myelogenous leukemia. Recently Fokas has been involved with the modeling of Covid-19. With Gelfand and others have introduced topological rules limiting severely the possible topological arrangements in protein folding of sandwich proteins.Interests and Research

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