Research
Preprints
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Handlebodies for the Painlevé Betti spaces with
Bill Olsen (2025)
We prove that the generic fibre of the Betti moduli space associated
to any of the ten Painlevé equations coincides with the result of
attaching Weinstein handles along the Stokes Legendrian, and provide
Weinstein handlebody diagrams for each of them. We also describe how
to obtain a Legendrian handlebody diagram in Gompf normal form of the
Legendrian lifts of curves in a surface with nonempty boundary.
Talks
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Definition of the partially wrapped Fukaya category,
Summer School on Partially Wrapped Fukaya categories, Helmsley, July 2025
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Introduction to quilted Floer homology,
Lagrangian Correspondences and Quilts, European Kylerec Oppdal, March 2025
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Open books and Lefschetz fibrations,
Junior Symplectic Geometry Seminar, ETH Zürich, 2021
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Delzant's classification of symplectic toric manifolds, University of
Tokyo, October 2019
Software
Ancient Writings
Material here is expository and no claim for either correctness or originality is made. The intent behind writing these was to explain the content of the paper they concern to a version of myself that had not read the paper, so they may be useful for students of a similar background.
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M.Sc. Thesis (2021)
An account of Lefschetz-Bott fibrations, based on this paper by Takahiro Oba. Covers a construction to obtain them and how they give a strong symplectic (but not Weinstein!) filling of their boundary.
- Semester Project (2020)
A detailed write-up (with more background for students) of this blog post by Terence Tao. Treats the Duistermaat-Heckman theorems (how the symplectic form changes when varying the level at which one does reduction), and how to use them to prove the Harish-Chandra-Itzykson-Zuber integral formula.
- B.Sc. Thesis (2019)
Essentially a review of Delzant's classification of symplectic toric manifolds and the Moser trick.