Embedded Files
The Hopf fibration, which can be understood in terms of a contact structure on the three-dimensional sphere.
Overview
Overview
I study symplectic topology and contact topology. Symplectic structures are 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.
Here are some recent Quanta articles about advances in and applications of symplectic and contact topology:
Preprints and publications
Preprints and publications
Hard Legendrian unknots.
(Joint with A. Christian and A. Wu.)
arXiv preprint (2026). (arXiv link)
Convex hypersurface theory in contact topology
(Joint with A. Christian, K. Honda, and Y. Huang.)
arXiv preprint (2026). (arXiv link)
Lagrangian slice disks with symplectomorphic exteriors.
arXiv preprint (2026). (arXiv link)
Regular Lagrangians in Lefschetz fibrations.
(Joint with A. Roy and L. Wang.)
arXiv preprint (2025). (arXiv link)
Non-orientable Nurikabe.
(Joint with E. Copeland.)
To appear in J. Comb. (arXiv link)
Regularly slice implies once-stably decomposably slice.
arXiv preprint (2024). (arXiv link)
Bypass moves in convex hypersurface theory.
(Joint with A. Christian.)
To appear in J. Symplectic Geom. (arXiv link)
Folded symplectic forms in contact topology.
J. Geom. Phys. 201:105213 (2024). (arXiv link) (Journal link)
The Giroux correspondence in arbitrary dimensions.
(Joint with K. Honda and Y. Huang.)
arXiv preprint (2023). (arXiv link)
Torus bundle Liouville domains are stably Weinstein.
(Joint with A. Christian.)
J. Topol. 18 (2025), e70052. (arXiv link) (Journal 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 with M. Bueno, S. Ford, and S. Furtado.)
Linear Algebra Appl. 519 (2017), 73-101. (Journal link)
Talks
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)
Page updated
Google Sites
Report abuse