I'm a Postdoctoral Research Assistant in the Structure and Symmetry Theme at the University of Edinburgh, in Scotland. I started here in September 2023 and am funded in part through the Simons Collaboration on Global Categorical Symmetries, and in part by my National Science Foundation (NSF) Postdoctoral Research Fellowship (DMS-2202753).
My research is mainly focused on using skein theory to understand (quantised) constructions in algebraic geometry and (again, quantum) non-semisimple topological invariants. One special interest of mine is defects in skein theory, which are useful for quantising constructions that involve parabolic reduction. Another special interest is q-holonomic systems which appear frequently in the construction of quantum invariants. I'm curious about their representation theoretic and physical origins.
These projects fall into a branch of math often called quantum topology. I also enjoy coding, you can find some of my old and ongoing projects on my github profile.
In June 2022 I was awarded a PhD in Mathematics at UC Davis, working with Motohico Mulase and Tudor Dimofte. My bachelors degree is in both math and physics and from Georgetown University, in Washington, DC. Marcos Rigol was my senior thesis adviser. Between degrees I worked for a couple years as a systems and infrastructure engineer at a tech company. (The company has since been acquired by Oracle.)
In my free time I enjoy backpacking, cooking, and gardening. My partner Benjamin Haïoun is also a mathematician!
Papers
- Defects in Skein Theory and the Quantum A-polynomial (DRAFT)
- Joint with David Jordan
- Skein Categories in Non-semisimple Settings
- Joint with Banjamin Haïoun
- Quantum invariants arising from Uhsl(2|1) are q-holonomic
- Joint with Nathan Geer
- The ADO Invariants are a q-Holonomic Family
- Joint with Tudor Dimofte, Stavros Garoufalidis, and Nathan Geer
- Driven dipole oscillations and the lowest-energy excitations of strongly interacting lattice bosons in a harmonic trap
- Joint with K. He, S. Haas, and M. Rigol
Talks
Seminars & Conferences
- Skein Categories in Non-semisimple Settings, January 13th, 2025 Topology Seminar at the University of Southern California. Los Angeles, California.
- Defects in Skein Theory and the A-polynomial, December 19th, 2024 Séminaire GADT at L’Institut de Mathématiques de Bourgogne. Dijon, France.
- Non-Semisimple Skein Categories, December 9th, 2024 Skein Days. Cergy-Pontoise, France.
- Skein Theoretic Quantization of the A-polynomial, December 5th, 2024 Geometry and Topology Seminar. Uppsala, Sweden.
- Non-semisimple Skein Categories, October 10th, 2024 Higher structures in Noncommutative Geometry and Quantum Algebra. Lille, France.
- Defects and the A-polynomial, September 4th, 2024 Recent Developments in Topological Quantum Field Theory at BIMSA. Beijing, China.
- Quantizing the A-polynomial, June 19th, 2024 Categorical symmetries in Quantum Field Theory at ICMS. Edinburgh, UK
- Orthogonal Knot Invariants, April 18th, 2024 Gauge Fields in Arithmetic, Topology and Physics at ICMS. Edinburgh, UK
- Defects and Quantized Character Stacks, October 17th, 2023 Complex Lagrangians, Mirror Symmetry, and Quantization at the Banff International Research Station. Banff, Canada
- Diagrammatics and Stratified Factorization Homology, June 13th, 2023 Séminaire de Géométrie et Topologie, Institut de Mathématics de Toulouse, France.
- Defects in Skein Theory, May 17th, 2023 Lisbon TQFTs Seminar. (Remote)
- Skein Theory and Quantized Knot Invariants, April 7th, 2023 Séminaire de Groupes, Représentations et Géométrie, Institut de Mathématiques de Jussieu-Paris Rive Gauche. Paris, France.
- Skein Theory and Quantizing Character Varieties, October 19th, 2022 Algebraic Geometry Seminar, University of Georgia. Athens, Georgia.
- Skein Categories and Quantization, April 13th, 2022 Emerging Researchers in Category Theory Seminar, Topos Institute. (Remote)
- Racks and Quantum Invariants, March 12, 2021 QMAP Seminar, UC Davis. Davis, CA.
- Recursion Properties of Quantum Invariants, October 2020 Informal Research Seminar, Institut Mittag-Leffler. Djursholm, Sweden.
- Knot Invariants, Quantum Groups, and the Knot Group, December 17, 2019 Greifswald Universitaet. Greifswald, Germany.
Lecture Series
- The Quantum A-polynomial, June 16th - 20th, 2025 Global Categorical Symmetries Summer School at the SwissMAP Research Station, Les Diablerets, Switzerland.
- Skein Theory, May 20th - 24th, 2024 Atlantic TQFT Spring School at the Atlantic Algebra Center, Memorial University New-foundland. St. Johns, Newfoundland, Canada.
Service
Ongoing
- Count-Me-In Project Lead Summer 2025 Work with a post-graduate student to mentor a group of undergraduate students on an independent research project. Design project, provide guidance in weekly meetings.
- Scottish Talbot Workshop Co-organizer, 2024, 2025 Co-organized participant led workshop held at the Glenmore Lodge in the Scottish Highlands.
- Edinburgh Algebra Seminar Co-organizer 2023 - Current.
Past
- REU Program Assistant Summers 2021, 2022 Supported a summer research program for 13 undergraduate students at UC Davis. Helped Organize and run field trips, handled bike assembly and repairs, and mentored students on their individual projects.
- Calculus Room Coordinator 2020-2021 academic year Ran the UC Davis math department's calculus help center. Set protocol for remote operations, coordinated shifts for about sixty TAs.
- Wilderness Guide 2017-2020 Led backpacking and snow camping trips for small groups, through the UC Davis Outdoor Adventures program.
- President of the Galois Group Summer 2018 - Spring 2020 Ran the student association for UC Davis math and applied math graduate students. Acted as the main point of contact for graduate concerns in the department, organized elections, office assignments, funding for student activites.
- Exam Accommodations Coordinator Fall 2018, Winter 2019 Organized exams for students allotted extra time on in-class assessments, for all upper division math courses at UC Davis. Coordinated with student accommodations office.