I’m interested in the development of asymptotic and stochastic methods in applied mathematics, especially for the fundamental study of atmosphere ocean fluid dynamics. Asymptotic methods arise if we cannot solve the problem we actually want to solve in an exact manner; often this involves partial differential equations. Instead, we solve a different problem that is “close” to the original problem in a suitable asymptotic sense.  Hopefully, the solution to the second problem is then close to the one we actually care about!  Such asymptotic methods might be analytical, numerical, or a combination thereof. Stochastic methods are a bundle of ingenious strategies that we can use to incorporate uncertainty and randomness into our exact mathematics.  This is very useful for many practical problems in arts & science where information is necessarily incomplete, for instance anything related to turbulence, quantum mechanics, or financial markets. Atmosphere ocean fluid dynamics.  If you know classical fluid dynamics then you might be surprised that there is an entire sub-discipline dedicated just to the geophysical fluid dynamics of atmosphere ocean flows.  It was only recognized in the twentieth century that the fluid flows on a rapidly rotating and strongly stratified spherical planet differ dramatically from the more familiar fluid flows on a human scale.   It was this insight that led to the first successful weather forecasts using computers.   If you know and like fluid dynamics then I’ll bet that you will like geophysical fluid dynamics!