- Assistant Professor at SLU 2023-
- NSF Postdoc and Chauvenet Postdoc at WashU 2019-23
- PhD Yale 2019
- BA UC Berkeley 2013
- Full CV
arXiv // Google Scholar // MathSciNet // ORCID
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From quasigeodesic to pseudo-Anosov flows
With Steven Frankel
In preparation -
Simultaneous universal circles
With Yair Minsky and Samuel Taylor
Submitted 2024 // 25 pages // arXiv -
Transverse surfaces and pseudo-Anosov flows
With Yair Minsky and Samuel Taylor
Submitted 2024 // 48 pages // arXiv -
Endperiodic maps, splitting sequences, and branched surfaces
With Chi Cheuk Tsang
Geometry & Topology, to appear // 144 pages // arXiv -
Endperiodic maps via pseudo-Anosov flows
With Yair Minsky and Samuel Taylor
Submitted 2023 // 50 pages // arXiv // most current version -
Flows, growth rates, and the veering polynomial
With Yair Minsky and Samuel Taylor
Ergodic Theory and Dynamical Systems Vol. 43, no. 9, pp. 3026-3107. 2023. journal, arxiv -
A polynomial invariant for veering triangulations
With Yair Minsky and Samuel Taylor
Journal of the European Mathematical Society Vol. 6, no. 2, pp. 731-788. 2024. journal, arxiv -
Veering triangulations and the Thurston norm: homology to isotopy
Advances in Mathematics, Volume 396, paper 108102, pp. 1-53, 2022. journal, arxiv. -
Stable loops and almost transverse surfaces
Groups, Geometry, and Dynamics, Vol. 17, No. 1, pp. 35-75, 2023. journal version -
Taut branched surfaces from veering triangulations
Algebraic and Geometric Topology, Vol. 18, pp. 1089-1114, 2018. arxiv
Earlier articles arising from undergraduate research:
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On symplectic capacities of toric domains
With Matthew McMillan and Emmanuel Tsukerman
Involve Vol 8 (2015), 665-676. arxiv -
Knot projections with a single multi-crossing
With C. Adams, T. Crawford, B. DeMeo, A. Tong Lin, M. Montee, S. Park, S. Venkatesh, and F. Yhee
Journal of Knot Theory and its Ramifications Vol. 24 No. 3, 2015. arxiv
This paper introduced petal projections. -
Perfect state transfer on quotient graphs
With E. Fredette, J. Fuller, M. Opperman, C. Tamon, and A. Tollefson
Quantum Information and Computation Vol. 12 Nos. 3&4, 2012. arxiv
- SLU Geometry and Topology Seminar
- ForALL, the SLU math department's semesterly math magazine
- Directly related to my research:
- Slides from a lightning talk about Endperiodic maps, splitting sequences, and branched surfaces (joint with Tsang) at Yair Minsky's 60th birthday conference in May 2023.
- A poster I made about the paper Endperiodic maps via pseudo-Anosov flows (joint with Minsky and Taylor). This was for a poster session at the workshop "Flexibility and Rigidity in Dynamical Systems" at the Simons Center in March 2022.
- NCNGT 2021 talk: "Limits of dilatations and depth one foliations." Video and slides.
- Slides from a talk I gave about the papers "Veering triangulations and the Thurston norm: homology to isotopy" and "A polynomial invariant of veering triangulations."
- Tangentially related to my research:
- I coörganized the St. Louis Topology Conference (17-19 May 2024). The theme was foliations and flows in 3-manifolds. I designed the conference poster and t-shirt.
- Thoughts on and images from my notebook
Written for the Fall 2024 issue of ForALL. - Seifert surfaces and genera of knots
Originally these were notes for an expository talk given at the Summer Undergraduate Mathematics Research at Yale (SUMRY) program in 2014, and later I adapted them to appear in ForALL in Fall 2023.
- Here are some videos I find cool and inspiring:
- Here is some great reading material:
- Gallery of the Infinite by Richard Schwartz
- The Shape of Space by Jeffrey Weeks
- Euler's Gem by David Richeson
- On proof and progress in mathematics by William Thurston
Photograph taken by Stefan Friedl.
The drawing is a draft figure from "Pseudo-Anosov flows from sutured hierarchies" with Tsang (in progress).
Research partially supported by the National Science Foundation.