Research

I am interested in low-dimensional topology and knot theory. Specifically I am focused on categorified invariants like Khovanov homology and knot Floer homology, the relationship between Khovanov homology and Floer theories, and using these invariants to study knots, links, and braids.

Publications/Preprints

• • • • Proof in the Age of Generative Production submitted preprint available upon request

      • Khovanov homology and Lagrangian cobordisms [arXiv:2412.15351] submitted (joint with  Ina Petkova and Zachary Winkeler)

      • Annular Khovanov homology and meridional disks [arXiv:2103.01269] Journal of Knot Theory and its Ramifications Vol. 32, no.2

      • Knot Floer homology, link Floer homology and link detection [arXiv:2011.02005] (joint with Fraser Binns) Algebraic & Geometric Topology Vol. 24, no.1 

      • Khovanov homology detects T(2,6) [arXiv:2005.02893] Mathematical Research Letters Vol. 29, no.3

      • Braids, fibered knots, and concordance questions [arXiv:2004.07445] (joint with Diana Hubbard, Keiko Kawamuro, Feride Ceren Kose, Olga Plamenevskaya, Katherine Raoux, Linh Truong, Hannah Turner) Proceedings Volume of the 2019 Research Collaboration Conference for Women in Symplectic and Contact Geometry and Topology.

      • Khovanov homology and causality in spacetimes [arXiv:2001.07274] (joint with Vladimir Chernov and Ina Petkova) Journal of Mathematical Physics Vol. 61, no. 2

      • Annular Rasmussen invariants: Properties and 3-braid classification [arxiv:1909.09245] Michigan Mathematical Journal Vol. 73, no. 3

As an undergraduate at Marlboro College I did summer research in combinatorics and co-authored two papers

• • • • R-sequencings and strong half-cycles from narcissistic terraces (joint with Matt Ollis)

      • Infinite Latin Squares: Neighbor Balance and Orthogonality (joint with Anthony Evans, Kaethe Minden, and Matt Ollis)]