A. Fokas

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Prof. Athanassios Fokas has 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 (1986). In 1996 he was appointed to a Chair in Applied Mathematics at Imperial College and in 2002 he was appointed to the newly inaugurated Chair in Nonlinear Mathematical Science at the University of Cambridge. In 2000, on the occasion of the millennium, he was awarded the Naylor Prize, which is the most prestigious prize in Applied Mathematics and Theoretical Physics in UK (the last recipient before Fokas was Stephen Hawking). He has published in different areas of science, ranging from classical areas of mathematics such as the introduction of a new approach to the celebrated Lindelöf'shypothesis, to applied areas such as models of chronic myelogenous leukaemia, protein folding, and mathematical models for Covid-19.He has introduced the transformative 'Fokas method' for solving partial differential equations and has played a pivotal role in the solution of several mathematical problems arising in medical imaging.

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Alokmay Datta

Saha Institute of Nuclear Physics

Alberto Pimpinelli

Université Clermont Auvergne

David Seamon

Kansas State University

Hai-Yao DENG

The University of Manchester

Alexandre Martin

University of Kentucky

Samit Chakrabarty

University of Leeds

Johannes Preiser-Kapeller

Austrian Academy of Sciences

Eugene Stanley

Boston University

Nikos Mantzakouras

National & Kapodistrian University of Athens

Yasser Shekofteh

Shahid Beheshti University

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Records of Proceedings at Meetings

Bulletin of the London Mathematical Society, 1998

held on Friday 20 June 1997 at the Linnean Society’s Rooms, Burlington House, Professor J. M. Bal... more held on Friday 20 June 1997 at the Linnean Society’s Rooms, Burlington House, Professor J. M. Ball, FRS, in the Chair. There were present about 35 members and visitors. Nine people were elected to Ordinary Membership: B. H. Bowditch, V. V. Goryunov, M. P. Joy, C. Knudsen, A. V. Mikhailov, B. P. Rynne, M. Sayed, V. M. Turner, K. A. J. White; two people were elected to Associate Membership: R. M. Green, A. G. Livotto; and three people were elected to Reciprocity Membership: L. Foschini (Unione Mat. Ital.), V. G. Miller (Amer. Math. Soc.), C. A. Semple (New Zealand Math. Soc.). The President, on Council’s behalf, proposed that Professor P. D. Lax be elected to Honorary Membership of the Society, and read the citation published below. He also announced, on Council’s behalf, the award of the 1997 Pólya Prize to Dr J. M. Hammersley, FRS, of the 1997 Senior Whitehead Prize to Professor J. H. Coates, FRS, of the 1997 Junior Berwick Prize to Dr H. D. Macpherson, and of 1997 Junior Whitehead prizes to Dr B. H. Bowditch, Dr A. Grigor’yan and Dr D. Joyce, and read short versions of the citations which are published below. Professor D. G. Quillen gave a lecture on ‘Module theory over nonunital rings’, and Professor J. P. May gave the 1997 Hardy Lecture on ‘Stable algebraic topology and stable topological algebra’.

CONFERENCE IN NUMERICAL ANALYSIS (NumAn 2007) RECENT APPROACHES TO NUMERICAL ANALYSIS: THEORY, METHODS AND APPLICATIONS

This volume contains a collection of extended and short abstracts of talks presented at NumAn 200... more This volume contains a collection of extended and short abstracts of talks presented at NumAn 2007. The Conference had as stated aims to bring together and bequeath scientific activities, directions and pursuits of Greek scientists in Greece and abroad on subjects that pertain to the conference; to foster an exchange of views and ideas; to study the theoretical background required for methods, algorithms and techniques used in applications; to search directions of theoretical results towards applications; to highlight open problems and future directions of numerical analysis. The volume also contains contributions by several international participants; we are grateful to them for choosing to contribute to this event. All this, in the magnificent surroundings of Kalamata, a wonderful city in the Messinia region of southern Greece. The majority of the papers deal (primarily) with computational topics in the areas of Linear Algebra, Partial Differential Equations and Optimization. There are also papers in Differential, Integral and Nonlinear Equations, Error Analysis, Approximation, and applications such as Fluid Dynamics, Weather Prediction, Statistics and Data Mining. Several distinguished senior speakers are invited to honor this conference. These are Professors N.

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A Bohr-type model with gravity as the attractive force

We formulate a Bohr-type rotating particle model for three light particles of rest mass mo each, ... more We formulate a Bohr-type rotating particle model for three light particles of rest mass mo each, forming a bound rotational state under the influence of their gravitational attraction, in the same way that electrostatic attraction leads to the formation of a bound proton-electron state in the classical Bohr model of the H atom. By using special relativity, the equivalence principle and the de Broglie wavelength equation, we find that when the three rotating particles have the rest masses of neutrinos or antineutrinos (∼ 0.05 eV /c 2) then surprisingly the rest mass of the rotating state has the rest mass of the stable baryons, i.e. of the proton and the neutron (∼ 1 GeV /c 2). This rest mass is due almost exclusively to the kinetic energy of the rotating neutrinos. The results are found to be consistent with the theory of general relativity. Predictions for the properties of these bound rotational states are compared with experimental values.

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A new immersion formula for surfaces on Lie algebras and integrable equations

Note on solutions to a class of nonlinear singular integro-differential equations

Physics Letters A

Certain classes of nonlinear singular integro-differential equations are considered. These equati... more Certain classes of nonlinear singular integro-differential equations are considered. These equations are mapped, via explicit transformations, to either ordinary differential equations or to linearizable partial differential equations. Permanent address: Program for Applied Mathematics, Princeton University, Princeton, NJ 08540, USA.

Bi-Hamiltonian Structures and Integrability

Springer Series in Nonlinear Dynamics, 1993

Mathematical physics 2000. International congress, London, GB, 2000

XIIIth international congress on mathematical physics. Proceedings of the ICMP 2000, Imperial College, London, Great Britain, July 17–22, 2000

Highlights of mathematical physics. In part papers from the 13th international congress, London, UK, July 17–22, 2000

Integrable nonlinear evolution partial differential equations in 4 + 2 and 3 + 1 dimensions

Physical review letters, Jan 19, 2006

The derivation and solution of integrable nonlinear evolution partial differential equations in t... more The derivation and solution of integrable nonlinear evolution partial differential equations in three spatial dimensions has been the holy grail in the field of integrability since the late 1970s. The celebrated Korteweg-de Vries and nonlinear Schrödinger equations, as well as the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations, are prototypical examples of integrable evolution equations in one and two spatial dimensions, respectively. Do there exist integrable analogs of these equations in three spatial dimensions? In what follows, I present a positive answer to this question. In particular, I first present integrable generalizations of the KP and DS equations, which are formulated in four spatial dimensions and which have the novelty that they involve complex time. I then impose the requirement of real time, which implies a reduction to three spatial dimensions. I also present a method of solution.

Nonlinear integrable equations and nonlinear Fourier transform

The Arnold-Gelfand Mathematical Seminars, 1996

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The inverse spectral method for the KP I equation without the zero mass constraint

Alternating regularisation in measurement-and image space for PET reconstruction

The dbar method

Theory and Application, 2003

Mathematical Physics 2000

On the Initial Value Problem of the Third Painlevé Equation

Research Reports in Physics, 1990

An isomonodromic Approach in the Theory of Two-Dimensional Quantum Gravity

The Focusing NLS Equation on the Half-Line with Periodic Boundary Conditions

We consider the Dirichlet problem for the focusing NLS equation on the half-line, with given Schw... more We consider the Dirichlet problem for the focusing NLS equation on the half-line, with given Schwartz initial data and boundary data $q(0,t)$ equal to an exponentially decaying perturbation $u(t)$ of the periodic boundary data $ a e^{2i\omega t + i \epsilon}$ at $x=0.$ It is known from PDE theory that this is a well-posed problem (for fixed initial data and fixed $u$). On the other hand, the associated inverse scattering transform formalism involves the Neumann boundary value for $x=0$. Thus the implementation of this formalism requires the understanding of the "Dirichlet-to-Neumann" map which characterises the associated Neumann boundary value. We consider this map in an indirect way: we postulate a certain Riemann-Hilbert problem and then prove that the solution of the initial-boundary value problem for the focusing NLS constructed through this Riemann-Hilbert problem satisfies all the required properties: the data $q(x,0)$ are Schwartz and $q(0,t)-a e^{2i\omega t + i \e...

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Painlevé transcendents: the Riemann-Hilbert approach

Page 1. Mathematical Surveys and Monographs Volume 128 Painleve Transcendents The Riemann-Hilbert... more

Generalized Dirichlet-to-Neumann Map in Time-Dependent Domains

Studies in Applied Mathematics, 2012

We study the heat, linear Schrödinger and linear KdV equations in the domain l(t) < x < ∞, 0 < t ... more We study the heat, linear Schrödinger and linear KdV equations in the domain l(t) < x < ∞, 0 < t < T , with prescribed initial and boundary conditions and with l(t) a given differentiable function. For the first two equations, we show that the unknown Neumann or Dirichlet boundary value can be computed as the solution of a linear Volterra integral equation with an explicit weakly singular kernel. This integral equation can be derived from the formal Fourier integral representation of the solution. For the linear KdV equation we show that the two unknown boundary values can be computed as the solution of a system of linear Volterra integral equations with explicit weakly singular kernels. The derivation in this case makes crucial use of analyticity and certain invariance properties in the complex spectral plane. The above Volterra equations are shown to admit a unique solution.

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Records of Proceedings at Meetings

Bulletin of the London Mathematical Society, 1998