5th Year Ph.D. Candidate, iCME
Relevant past/current employment:
Graduate Technical Intern, Aerosciences Dept.,
Sandia National Lab, Albuquerque, NM (06/2007-present)
Teaching Assistant, Mathematics Department, University of Pennsylvania, Philadelphia, PA (09/2005-05/2006)
Actuarial Intern, Watson Wyatt Worldwide, Southfield, MI (06/2004-08/2006)
National Defense Science and Engineering (NDSEG) Fellowship (2007 recipient)
National Physical Science Consortium (NPSC) Fellowship (2007 recipient)
My background, and what led me to applied/computational math:
I started out as a (pure) mathematics major at the University of Pennsylvania
(U Penn). At first, I considered a career
as an actuary. I minored in actuarial science at the
Wharton School of Business, began taking the actuarial exams,
and did two internships at Watson Wyatt Worldwide,
an actuarial consulting firm - only to realize the acturial
profession is not for me, and that my true passion was in research/teaching.
After completing the requirements
for my Bachelors at the end of three years, I
submatriculated into the Masters program at U Penn's math
department. While working on my
I began to find it bothersome that the work I was doing, while interesting in its own
right, had little relevance to the physical world. This made me think a Ph.D. program
where I would be able to apply my knowledge of mathematics to problems
of practical relevance in the sciences and
engineering would be a better fit for me than a graduate program in pure mathematics.
I applied to close to a dozen Ph.D. programs in applied/computational
math but the choice ultimately came down to Stanford's iCME (Institute
for Computational & Mathematical Engineering) and Princeton's PACM
(Program in Applied & Computational Math). I chose iCME for its breadth and the diversity
of the research done by the affiliated faculty. Having had limited exposure to
engineering applications in my Bachelors/Masters work,
I wanted a program where I would have the chance to explore various areas before settling on a research topic.
I felt the structure of the iCME program encouraged this type of academic exploration.
I was not sure if I would have the same opportunity at a university with a smaller applied math/engineering program,
where the faculty interests are often less varied.
What I work on (in a nutshell):
My research focuses on developing and improving numerical methods to solve partial differential
equations (PDEs), the equations of fluid mechanics (the advection-diffusion equation, the Euler equations, the Navier-Stokes equations, etc.)
in particular. In certain
flow regimes, namely advection-dominated flows (high speed flows with just a little bit of viscosity),
classical methods like the finite element method (FEM) are in general inadequate unless the mesh is refined substantially.
The aim of my work is to try to come up with variants of these methods that will work better,
meaning will be able to produce a good computed solution at a low computational cost (i.e., fast)
in these difficult flow regimes. If you want to know more, a more
detailed description of my research can be found here.
Advice for prospective students:
In terms of choosing a grad school, definitely visit the places you are considering and
talk with the students. You get a much better sense of whether or not a particular
university is the place for you when you actually go there and meet some of the people in person.
I also highly recommend applying for external (e.g., national) fellowships (NSF, NDSEG, NPSC, etc.).
Having your own funding gives you the opportunity to work with whomever you
choose to work with and frees you from graduate duties like grading.
general piece of advice: try not to be overwhelmed by the whole application process, and
not know exactly what
you want to do, if you are still exploring various options. Most people do not know exactly who
they want to work with, what their dissertation topic will be, etc. when they first begin grad school.
Extracurricular interests & activities:
Hiking, swimming, traveling, cars/driving.
Post graduation aspirations/plans:
Definitely a research position, either in academia or at a national lab.
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