Research

The Hopf fibration, which can be understood in terms of a contact structure on the three-dimensional sphere.

Overview

I primarily study symplectic topology and contact topology. Symplectic structures arise from the mathematical abstraction of Hamiltonian mechanics, and symplectic manifolds are even-dimensional objects that generalize phase space. Contact manifolds are the odd-dimensional siblings of symplectic manifolds --- they have their own physical motivation, but also, for example, arise naturally as hypersurfaces in symplectic manifolds.

I'm interested in furthering our knowledge of contact and symplectic structures in high dimensions, where less about them is known, but I'm also becoming increasingly interested in their interactions with low-dimensional topology.

Here are some recent Quanta articles about recent advances in and applications of symplectic and contact topology:

Preprints and publications

Non-orientable Nurikabe.

(Joint work with E. Copeland.)

arXiv preprint (2025). (arXiv link)

Regularly slice implies once-stably decomposably slice.

arXiv preprint (2024). (arXiv link)

Bypass moves in convex hypersurface theory.

(Joint work with A. Christian.)

arXiv preprint (2024). (arXiv link)

Folded symplectic forms in contact topology.

Journal of Geometry and Physics, 201:105213 (2024). (arXiv link) (Journal link)

The Giroux correspondence in arbitrary dimensions.

(Joint work with K. Honda and Y. Huang.)

arXiv preprint (2023). (arXiv link)

Torus bundle Liouville domains are stably Weinstein.

(Joint work with A. Christian.)

arXiv preprint (2021). (arXiv link)

Morse-Smale characteristic foliations and convexity in contact manifolds.

Proc. Amer. Math. Soc. 149 (2021), 3977-3989. (arXiv link) (Journal link)

On the sign characteristic of Hermitian linearizations in DL(P).

(Joint work with M. Bueno, S. Ford, and S. Furtado.)

Linear Algebra and its Applications, 519 (2017), 73-101. (Journal link)

Talks

Video of a talk about the Giroux correspondence at a Banff workshop: (video link)
Video of a talk about the Giroux correspondence in the University of Minnesota seminar: (video link)
Slides for Panorama of Topology, University of Iowa 2024: (pdf link)

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