|Hometown:||Moscow, Russia/West Bloomfield, MI|
|At Stanford since:||September 2006|
|Education:||Ph.D. CME, Stanford, June 2011 (Graduated)|
|M.A. Mathematics, U Penn, May 2006|
|B.A. Mathematics, U Penn, May 2006|
|Advisor:||Dr. Charbel Farhat|
|Research Area(s):||Hybrid Discontinuous Finite Element Methods|
|Research Group(s):||Farhat Research Group (FRG)|
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 Masters thesis, 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.
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.
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. A more 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.
Hiking, swimming, traveling, cars/driving.
Definitely a research position, either in academia or at a national lab.