|
I am an Assistant Professor in the Mathematics department at Princeton University. Before coming to Princeton in Fall 2017, I was an RTG Instructor at the University of Texas at Austin. I received my Ph.D. from Columbia University in 2014, supervised by Robert Lipshitz. View my CV I am currently teaching MAT 104: One-Variable Calculus with Proofs. I help organize the Princeton Topology Seminar. In summer 2023 I co-organized the RTG Summer School in Geometry and Topology. |
 |
|
My research interests lie in low-dimensional topology. I am particularly interested in knots and 3-dimensional manifolds,
and I focus on using Heegaard Floer homology and related invariants to study these objects.
Much of my work focuses on problems that relate to cutting and gluing 3-manifolds or knots.
This includes questions about Dehn surgery (the process of removing and reattaching the neighborhood of a knot)
and studying 3-manifolds by decomposing them along essential surfaces into manageable pieces.
See my papers and preprints Just for fun, I asked Google NotebookLM to make a podcast overview of my research (the only inputs were PDFs of all of my papers). Obviously, accuracy not guaranteed. I have written some code for computing Heegaard Floer invariants that may be useful to others, see more here. In particular, I have posted the knot Floer complex for all knots through 15 crossings for convenient reference. (While most of my computations are done digitally, I built an analog device that computes the knot Floer complex of some cables and 1-bridge braid satellites, pictured to the left) |