Research

My research interests are in low-dimensional topology and symplectic/contact geometry. Most recently I have been thinking about trisections of 4-manifolds, group trisections, and Lagrangian cobordisms between Legendrian knots. For a layperson’s “explainer” on some of the context in which my research sits, check out this awesome Quanta article (in which I was quoted!).

Publications & Preprints

  1. “A group-theoretic framework for low-dimensional topology”
    • Joint work with Robion Kirby, Michael Klug, Vincent Longo, Benjamin Ruppik. In this project, which began at the Summer Trisectors Workshop in 2020, we detail how to recover a bridge trisected surface in a 4-manifold from its group trisection.
  2. “Constructions of Lagrangian cobordisms”
    • Joint with my group from the WiSCon workshop in 2019: Noémie Legout, Caitlin Leverson, Maÿlis Limouzineau, Ziva Myer, Yu Pan, Samantha Pezzimenti, Lara Simone Suárez, and Lisa Traynor.
  3. “Good Reduction of Preperiodic Points”
    • During my senior year at St. Louis University I completed an independent research project on dynamical systems under the guidance of Benjamin Hutz.
  4. “A Generalization of a Method of Mordell to Ternary Quadratic Forms”
    • In the summer of 2015 I participated in WADE Into Research, a number theory REU.  My group studied ternary quadratic forms, and our work led to a paper and several presentations. Joint with Gabriel Durham, Katherine Thompson, and Tiffany Treece.

Recent Talks

Western Hemisphere Virtual Symplectic Seminar 2022
Tech Topology Summer School 2021
Young Topologists Meeting 2021
Two knot diagrams representing Legendrian knots that have the same classical invariants, but are not Legendrian isotopic
Two knot diagrams representing Legendrian knots that have the same classical invariants, but are not Legendrian isotopic
A diagram for a right-handed Legendrian trefoil with one of the polygons involved in the calculation of the Chekanov DGA differential shaded in
A diagram for a right-handed Legendrian trefoil with one of the polygons involved in the calculation of the Chekanov DGA differential shaded in

Recent & Upcoming Travel

I co-organized GOATS, a virtual mini-conference series for graduate students in topology and geometry, held on April 25, June 6, and July 18. See details here.

Here are some postcards I made for NGNCT 2021.