I'm a lecturer at the University of St Andrews in the School of Mathematics and Statistics. I grew up in Cardiff-by-the-Sea, California before getting my MA at UCLA and PhD at UC Berkeley under Denis Auroux.
I study the relation between symplectic, algebraic, and tropical geometry via mirror symmetry.
Outside of mathematics, my hobbies include playing piano, partner dancing, board games, and puzzles.
An outline of my research and teaching experience can be found in my CV.
Homological mirror symmetry predicts that symplectic geometry should be related to complex geometry on a mirror space via mutual comparison to tropical geometry on the base of an SYZ fibration. My research focuses on applying this correspondence to study problems in complex geometry. I'm currently looking at how to interpret realizability criteria in tropical geometry from a Lagrangian perspective; and how Morse theory in symplectic geometry relates to resolutions of coherent sheaves on a mirror space.
Monotone Lagrangian cobordisms provide equivalences in the Fukaya category. My current research is extending this equivalence to unobstructed Lagrangian cobordisms, with the goal of algorithmically constructing these equivalences in terms of the surgery handle decompositions for Lagrangian cobordisms. I'm also interested in quantitative aspects of Lagrangian cobordisms.
I've taught a variety of undergraduate courses and supervised masters and reading projects. I've also designed a course on combinatorial topology at UC Berkeley in Spring 17. If you are interested in using some of my course materials, please contact me and I can provide you with the source material.
In 2014, I started up the Berkeley Mathematics Directed Reading Program along with Nick Ramsey and Alex Youcis. In addition to being a program organizer through 2017, I have mentored several students through the DRP program. I also have had several research undergrads.
I have mentored for several summers at Canada-USA Mathcamp and was the 2018 academic program coordinator with Apurva Nakade. I've also taught for the Prison University Project, the Los Angeles Math Circle, and organized Splash at UCLA.
Symplectic snippets is a proof-of-concept for organizing some of my mathematical notes on symplectic geometry. It was initially put together for the PIMS Summer School on Floer Homotopy theory. Notes are written as whole articles in LaTeX and then processed into mathematical tags -- snippets -- which can be individually referenced by other articles. The site is available here.
Floer theory and Lagrangian cobordisms(Simons 2022)
Exact Sequences in Symplectic Geometry(PIMS 2022)
A sketch of Symplectic cohomology(PIMS 2022)
A sketch of Heegaard Floer(PIMS 2022)
Realizability and Obstruction in Tropical Geometry (2021)
Lagrangian Mutation and Cobordism (2021)
Lagrangian Cobordism and Lagrangian Surgery (2021)
Generating the Mirror to a Toric Variety (Stanford 2020)
Counting Disks on Lagrangian Cobordisms (ETH 2019)
Tropical Lagrangian Submanifolds (Montreal 2019)
Homological Algebra (Course from Mathcamp 2019)
Combinatorial Topology (Being Updated!)
St Andrews Pure Mathematics Colloquium (2025-) co-organizer with Natalia Jurga
Scottish Topology Seminar 25 co-organizer with Sukjoo Lee
EDGE Seminar (2022-2023) co-organizer
Hodge Seminar (2021-2023) co-organizer
Student Symplectic Seminar (2016) organized with Morgan Weiler
SFT Seminar (2016) with M. Weiler, C. Cannizzo, and B. Gammage
Please feel free to contact me at anytime if you have questions about the possibility of working together.
I will have a postdoctoral position available Fall 2026 at the University of St Andrews through EP/Z53528X/1. Please contact me directly if interested.
I will have another PhD position available in Fall 26 - details to come!
office: 316 Mathematical Institute, St Andrews
email:
office hours: by appointment
American Institute of Mathematics, HMS and MG Comm. Alg, 18 Aug 2025
