Prof Jon Chapman (University Oxford)

Exponential asymptotics and applied mathematics

Divergent series are the invention of the devil, and it is shameful to base on them
any demonstration whatsoever.” – N. H. Abel.
The lecture will introduce the concept of an asymptotic series, showing how useful divergent
series can be, despite Abel’s reservations. We will then discuss Stokes’ phenomenon, whereby
the coefficients in the series appear to change discontinuously. We will show how
understanding Stokes’ phenomenon is the key which allows us to determine the qualitative
and quantitative behaviour of the solution in many practical problems. Examples will be
drawn from the areas of surface waves on fluids, crystal growth, dislocation dynamics, HeleShaw flow, thin film rupture, quantum mechanics, and atmospheric dynamics.