Following, in the early 1980s, the extension of the Inverse Scattering Method  so that it could be applied to integrable nonlinear evolution equations  in two special dimensions (like the KP and the DS equations), the most important open problems in the analysis of integrable PDEs became the following: first, solving boundary as opposed to initial value problems and second constructing and solving integrable PDEs in three spatial dimensions.  The solutions of these key problems appeared in two publications by the speaker in the Proceedings of the Royal Society in 1997 and 2022 respectively. The former publication gave rise to a new method for solving boundary value problems for linear and for integrable nonlinear PDEs, the so-called Unified Transform (also known as the Fokas method).

For linear PDEs, the relevant transform is based on appropriate deformations of certain integrals from the real line to the complex plane. The idea of deforming to the complex plane has recently led to unexpected and exciting results regarding the large t-asymptotics of the celebrated Riemann zeta function.

Professor Thanasis Fokas is a chair professor in Nonlinear Mathematical Science in the Department of Applied Mathematics and Theoretical Physics (DAMTP) at the University of Cambridge. He previously served as the Chairman of the Department of Mathematics and Computer Science at Clarkson University (USA) and as a chair professor at Imperial College London. He is a member of the Academy of Athens and the Academia Europaea, and a Fellow of Clare Hall, Cambridge, the Guggenheim Foundation, the American Institute for Medical and Biological Engineering, and the American Mathematical Society.

 Professor Fokas has made outstanding contributions to science, medicine, and the arts, including advances in partial differential equations, mathematical physics, the life sciences, nuclear imaging for diagnosis and discovery, as well as his work in explaining and vividly communicating science and mathematics to the public. He has received the Naylor Prize from the London Mathematical Society, the Blaise Pascal Medal from the Academia Europaea, the Kruskal Award from the Society for Industrial and Applied Mathematics, and the Distinguished Alumnus Award from the California Institute of Technology.