knots

The last time UC Davis saw me was when graduated in the summer of 2018 with a Ph.D. in Mathematics. My dissertation was in low-dimensional topology under Abby Thompson, focusing on Heegaard splittings of knot complements in the 3-sphere (with additional mentorship of Javier Arsuaga in the application of knot theory to molecular biology, particularly the folding of chromosomes in yeast). Only a few months prior to that, I had accepted an offer to join the faculty at University of the Pacific (UOP) in Stockton, CA, as a tenure-track assistant professor of applied mathematics.

It has been another busy year for our undergraduate mathematics programs, with many exciting changes on the horizon. This year, our Undergraduate Program Committee is leading teams of faculty members in a review of all four of our majors – Mathematics, Applied Mathematics, Analytics and Operations Research, and Scientific Computation – with a view towards modernizing and improving what our current programs offer. The intent is to both add breadth to our current course offering, and to add support to mathematics students in the form of discussions across all of our classes.

I recently completed my Ph.D. in Mathematics at Georgia Tech, where I was advised by Jen Hom. My research focuses on problems in low-dimensional topology, primarily from the perspective of knot Floer homology and bordered Heegaard Floer homology. At UC Davis, I look forward to working with Melissa Zhang and broadening my approach by exploring new tools for studying knots and links in 3- and 4-manifolds.

Melissa Zhang is a low-dimensional topologist who likes to use algebraic, combinatorial, and categorical methods to solve problems. Her favorite topological objects are knots and surfaces smoothly embedded in 3- and 4-dimensional spaces.

She received her Ph.D. from Boston College under the supervision of Eli Grigsby and David Treumann. She was previously a postdoc at the University of Georgia, SLMath/MSRI, and UC Davis (and is now a super-postdoc, as she never left).