I am a graduate student in the math department at Brown University working with Govind Menon (in applied math). I will be graduating in May 2017. I was awarded an NSF Graduate Research Fellowship in 2011.
My research is in the field of probability, and I particularly like problems with links to mathematical physics, including those involving random maps (which are basically random graphs embedded on Riemann surfaces), Loewner evolution (both deterministic and SLE), and random matrix theory.
In my thesis, I prove that a certain random time-dependent real measure generates embeddings of Galton-Watson trees in the upper half-plane when used as the driving measure in the chordal Loewner equation. The Stieltjes transform of this measure turns out to satisfy a particular SPDE, and using this SPDE I conjecture the limit of the random measure as the Galton-Watson trees are rescaled to converge to the continuum random tree (CRT). I am currently investigating whether the hull generated by this limiting measure is an embedding of the CRT.
You can email me at vhealey"at"math.brown.edu. Here's a link to my CV.