University of Birmingham > Talks@bham > Applied Mathematics Seminar Series > Beyond integrability: the far-reaching consequences of thinking about boundary conditions

Beyond integrability: the far-reaching consequences of thinking about boundary conditions

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This talk is a School of Mathematics Colloquium

In this talk, I will outline results obtained in the last fifteen years, all stemming from the original aim to include the consideration of boundary conditions in the celebrated Inverse Scattering Transform, which is in essence a nonlinear Fourier transform.

The talk will revisit the Fourier transform on R, embedding it in a general way of thinking about integral transform that relies on a formulation in the complex domain (called a Riemann-Hlbert formulation) and start from this to describe a generalised approach, now known as the unified transform, or Fokas transform. These ideas yielded unexpected and very general results for the rigorous inversion of integral transform, for the solution of linear boundary value problems, for the study of nonselfadjoint differential operators, as well as for the original nonlinear problems. I will describe the key ideas and some of the most surprising outcomes.

This talk is part of the Applied Mathematics Seminar Series series.

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