Student Research

Doing research in analysis and PDE typically requires an unreasonably strong background, but I have some projects available which should be suitable for many undergraduates. The projects involve exploring some global properties of free boundaries and shape optimization problems using qualitative/numerical methods. If you meet most of the following criteria and are interested, email me to discuss further.

• You are a Rutgers undergraduate (or possibly an undergraduate at another local institution).
• You are well-versed in linear algebra and multivariable calculus.
• You know what partial differential equations are.
• You have some programming experience. Ideally in numerical PDE, more likely in numerical linear algebra and optimization, but even just general programming competency is enough.
• You have a reasonable amount of free time to dedicate to this, strong motivation, and ability to work independently.

I also have a different set of projects for students with unusually strong analysis backgrounds. These involve regularity and local properties of free boundaries and parabolic equations. If you meet most of the following criteria and are interested, email me to discuss further.

• You are a Rutgers or local undergraduate (graduate students see below instead).
• You have taken graduate-level analysis, functional analysis, and PDE courses (maybe not all of these, but at least some and some familiarity with the rest).
• You are familiar with energy methods, Sobolev spaces, the maximum principle, etc.

If you are a Rutgers graduate student interested in working with me, email me to arrange a meeting. Your background in this case does not matter, but you should be aware of what elliptic PDE are and have some interest in working on them.