Dr Simon Myerson
Warwick Zeeman Lecturer
Teaching Responsibilities 2020/21:
Term 1: MA3A6 Algebraic Number Theory
Research Interests: Analytic number theory, Diophantine problems, the circle method, dispersive PDEs, Strichartz estimates
I study the solutions to equations and inequalities in whole numbers. These are called Diophantine problems and they’re part of number theory. I use “analytic” arguments which are often fairly elementary, which makes it analytic number theory.
I’ve become interested in something which seems very different: nonlinear dispersive partial differential equations (nonlinear dispersive PDEs). This is a type of mathematical model which describes physical systems from ocean waves to fibre optic cables.
It is possible to apply analytic number theory to study these PDEs. This is because of the importance of Strichartz-type estimates in understanding dispersive equations. For PDEs posed on a torus (think water waves in a rectangular tank) these can be interpreted as discrete restriction estimates of a type also studied in number theory. These estimates are interpreted in terms of exponential sums, oscillating functions with intermittent large peaks.
These ideas are the basis of my Leverhulme Early Career Fellowship. The project has three independent, mutually beneficial parts: delivering novel Strichartz-type estimates with applications to PDEs; enhancing the number-theoretic toolkit used to produce them; and pushing beyond the case of the torus to other manifolds.