I received my bachelor's degree from Princeton University in June 2012. In my undergraduate thesis, which was supervised by John A. Baldwin and Peter S. Ozsváth, I re-derived Ciprian Manolescu's unoriented skein exact triangle for knot Floer homology (over Z/2Z) combinatorially, using grid diagrams. I extended the skein exact triangle to combinatorial knot Floer homology over Z, illustrated the spectral sequence that results from the iteration of the triangle, and gave another proof of a result on the Floer-homological σ-thinness of quasi-alternating links, due to Manolescu and Ozsváth. The paper is available here.
More recently, I have been working on extending the unoriented skein exact relation above to related contexts. Ina Petkova and I have established the analogous statement for tangle Floer homology. The paper is available here. I gave a talk on this result in the AMS 2015 Fall Central Sectional Meeting at Chicago and the AMS 2016 Fall Western Sectional Meeting at Denver, and here are the slides I wrote for the talks.
In another direction, I have also extended the unoriented skein exact triangle to unoriented grid homology over Z/2Z. Unoriented grid homology is a multi-pointed version of unoriented knot Floer homology, defined by Ozsváth–Stipsicz–Szabó, which corresponds to the t=1 case of modified knot Floer homology. A paper is forthcoming.
In the summer of 2010, I was involved in the Analysis of Fractals REU, organized by Alexander Teplyaev, at the University of Connecticut. I worked with Benjamin Steinhurst and Daniel Kelleher. We studied the relationship between self-similar groups and self-similar structures, and produced a result on constructing a self-similar group whose limit space has a given self-similar structure. I gave a talk on this result in the AMS 2010 Fall Eastern Sectional Meeting at Syracuse, and here are the slides I wrote for that talk.
I wrote an introduction to topology, which formed a part of the guide for mathematics majors, for the Princeton University Mathematics Club.
While I was at Princeton, my main extra-curricular activity was the Princeton University Glee Club (the university concert choir), in which I sang as a bass.
I also enjoy photography, playing bridge (which my former suitemate taught me) and playing table tennis.