So, applied mathematics is the use of the language of mathematics
to solve real world problems, or to study real world problems.
It’s sort of a gray area between the language of mathematics
and, you know, theoretical sides of other applications.
We are doing mathematics to help other sciences forward
and that can be applications to engineering,
to biology, to physics, to chemistry, any field, you name it.
It’s collaboration that’s more organic and more integrated.
Of course I need people who can do experiments,
who are good at doing experiments, and they need people that have more quantitative skills.
At UC Santa Cruz what we try and do is help our colleagues.
I’m currently collaborating with Mark Akeson and Kate Lieberman’s lab
in the Biomolecular Engineering Department, modeling single molecule experiments.
Basically we try to understand the mechanism, the physical mechanism, of DNA polymerase.
Yeah, we have some lofty aspirations.
So I work on fluid dynamics.
Fluid dynamics is fun because fluid dynamics is everywhere,
the air we breathe, the blood that’s coursing through our veins.
And of course this doesn’t only apply to Earth, it applies to other planets.
I have always this kind of dual identity as an astrophysicist and an applied mathematician.
Because I do research in fluid dynamics with application to astrophysics,
there is no way to do experimentation in the lab to see what this kind of fluid would do.
Even though the equations are the same,
they behave in a way that’s completely different from what, say, water or air would do.
And so we really, really need the numerical machinery,
and specifically high performance computing,
to be able to do essentially what’s called a numerical experiment.
There’s a big advantage to doing numerical simulations
in that an experiment with an observation you may only have access
to a small amount of information from that experiment.
You can only see certain things.
Whereas in a numerical simulation you can see everything.
So now what a lot of what academia and industry
is looking for is not only people who can make mathematical models,
but people who know how to solve those mathematical models on modern computing architecture.
It’s a very, very marketable skill.
It sounds like high performance computing is a buzzword,
it’s like a big word that sounds like fantasy, but it’s actually not.
So my main research area in applied mathematics is called computational mathematics.
This is one of the main applied mathematics area that heavily relies on using high performance computing actually.
There are many different types of applications that my research areas can contribute.
The research that I do, and the code that I develop actually has been tested on very large scale computers.
For instance, you can use this kind of computational mathematics
in order to solve supernova explosions in the universe.
Researchers in Applied Math, and our whole department of Applied Mathematics and Statistics,
and indeed across the whole Baskin School of Engineering, are very, very tenacious.
This tenacity means a lot of stuff gets done here on campus.
I mean students are literally working in parallel with the faculty at all stages of this process.
If you really want to investigate new areas, you somehow need new novel ideas.
That is, I think, the focal point in modern science
and that’s really happening within this Applied Mathematics and Statistics Department in UC Santa Cruz.
