Broadly speaking, my focus is to develop and apply advanced mathematical techniques in support of science and engineering generally, and particularly in geophysical applications. My primary areas of application are ocean modeling, data assimilation, and geophysical fluid dynamics. My main mathematical tools are multiscale and stochastic modeling, asymptotic analysis, Bayesian statistics, and numerical analysis. My publications are available at Google Scholar and on my ORCID profile. (If you are a prospective student interested in my publications, I recommend sorting by date rather than by citation count [the default], so you can see what I've been doing recently.)
Many conferences have recently adopted a format where presenters record and upload their presentation. Since I've already recorded these talks, I might as well make them publicly available. You can find them on my YouTube channel.
Apologia Pro Mathematica Applicantur
What is applied math? Isn’t it true that all of math can be applied to one thing or another? Certainly. Some math is more applicable than others, but in principle all math can be applied to something. Which points out the first thing about applied math: It is not the same as applicable math, otherwise all math would be applied math. It also means that applied math does not consist of a subset of mathematical subjects that has historically been more broadly applicable than other areas of math.
What does it mean to "do" applied math? When I am doing applied math I am using math to answer questions in fields other than mathematics. It could be argued that using math to answer questions in fields other than mathematics is not math at all, that it is ‘just’ science. On the other hand, developing new math that might be applied to something someday is not applied math. Applied mathematicians can both apply mathematics and develop applicable mathematics. But to say that using math to answer practical questions is not 'doing math' is directly contrary to the common meaning of the phrase 'do the math.'
Most of science and engineering requires the use mathematics, so are all scientists and engineers applied mathematicians? Who gets to call themselves an applied mathematician? I won't attempt to say who can't call themselves an applied mathematician. I claim to be an applied mathematician because I address problems in science and engineering that require more mathematical effort than a typical scientist in the same field is either willing or able to expend.