Keith Rogers

Biography

"Keith grew up on the west coast of Scotland and completed his degree in mathematics at the University of Edinburgh in 1999. After a master's year at the University of Cambridge, he obtained his PhD in 2004 from the University of New South Wales in Sydney. In 2011, Keith was awarded a Starting Grant by the European Research Council. Keith's speciality is Fourier Analysis; the art of recomposing a signal from its decomposition into different frequencies. This technique underpins quantum mechanics, and so a great deal of Keith's research has concerned the fundamental properties of Schrödinger and wave equations. However, Fourier Analysis can also be used to attack more basic questions, like his extension of the Fundamental Theorem of Calculus in three or more dimensions. This joint work with Javier Parcet was published in the Proceedings of the National Academy of Sciences USA. Fourier Analysis is also fundamental to the make-up of a number of developing technologies and Keith has redirected part of his energy in this direction. He recently solved an outstanding problem in Inverse Problems, conjectured by Uhlmann in the International Congress of Mathematicians in 1998, proving that an imaging technique, known as Electrical Impedance Tomography, can be expected to produce faithful images of relatively rough (Lipschitz) objects. This joint work with Pedro Caro was published in the Forum of Mathematics Pi. "

Research Interest

Directional maximal operators, convergence of Fourier integrals and series, the wave and Schrödinger equations, geometric measure theory, inverse problems