Research

Overview

I am interested in the topology of 2-, 3-, and 4-dimensional manifolds. I am primarily interested in dimension four, and here my work has centered around trisections of 4-manifolds. In dimension three, my main interests are Heegaard splittings. In two dimensions, I am mainly interested in the mapping class group and complexes associated to curves on a surface. For a more detailed overview see my research statement. 

Publications and Preprints:

  1. Multisections of 4-manifolds.
         (with Patrick Naylor) (arxiv)

  2. Representing smooth 4-manifolds as loops in the pants complex.

        (with Michael Klug) Submitted. (arxiv)

  3. The Relative L-invariant of a compact 4-manifold.

        (with Nick Castro, Maggie Miller, and Maggy Tomova) Submitted. arXiv:1908.05371(arxiv)

  4. Nielsen Equivalence and Trisections of 4-manifolds.

        Submitted. arXiv:1804.06978v2  (arxiv) 

  5. Comparing 4-Manifolds in the Pants Complex Via Trisections.

       Algebr. Geom. Topol. 18 (2018), no. 3, 1799--1822 (arxiv) (journal)
  6. The Khovanov Homology of Infinite Braids.
        (with Mike Willis) Quantum Topol. 9 (2018), no. 3, 563--590 (arxiv) (journal)