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
Multisections with divides and Weinstein 4-manifolds. with L.Starkston
Accepted to J. Symplectic Geom . arXiv:2303.00906 (arxiv)
Toric multisections and curves in rational surfaces. with H. Karimi, P. Lambert-Cole, and J. Meier
Accepted to Indiana Univ. Math. J . arXiv:2206.04161 (arxiv)
Uniqueness of 4-manifolds described as sequences of 3-d handlebodies.
Accepted to Mich. Math. J. arXiv:2111.08924 (arxiv)
Multisections of 4-manifolds. with P. Naylor
Accepted to Tran AMS. arXiv:2010.03057 (arxiv)
Representing smooth 4-manifolds as loops in the pants complex. with M. Klug
Math. Res. Lett. 28 (2021), no. 6, 1703--1738 (arxiv) (journal)
The relative L-invariant of a compact 4-manifold. with N. Castro, M. Miller, and M. Tomova
Pacific J. Math. 315 (2021), no. 2, 305--346 (arxiv) (journal)
Nielsen equivalence and trisections of 4-manifolds.
Geom. Dedicata 214 (2021), 303--317. (arxiv) (journal)
Comparing 4-manifolds in the pants complex via trisections.
Algebr. Geom. Topol. 18 (2018), no. 3, 1799—1822 (arxiv) (journal)
The Khovanov homology of infinite braids. with M. Willis
Quantum Topol. 9 (2018), no. 3, 563--59 (arxiv) (journal)
