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Jeff Hicks

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.

Research

Applications of Mirror Symmetry

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.

Lagrangian Cobordisms

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 quantiative aspects of Lagrangian cobordisms.

Publications and preprints

  1. Rigidity and Realizability for Tropical Curves in Dimension 3. Submitted. arXiv:2502.16582
  2. Homological mirror symmetry for Batyrev mirror pairs. (with Sheel Ganatra, Andrew Hanlon,Daniel Pomerleano, and Nick Sheridan ). arXiv:2406.05272
  3. Integrality of mirror maps and arithmetic homological mirror symmetry for Greene--Plesser mirrors. (with Sheel Ganatra, Andrew Hanlon,Daniel Pomerleano, and Nick Sheridan ). Submitted. arXiv:2312.01949
  4. A short computation of the Rouquier dimension for a cycle of projective lines. (with Andrew Hanlon). Proceedings of the American Mathematical Society
  5. Relating categorical dimension in topology and symplectic geometry. (with Andrew Hanlon, Oleg Lazarev). Submitted. arXiv:2308.13677
  6. Reverse isoperimetric ineq. for Lagrangian intersection Floer theory. (with Jean-Philippe Chassé, Yoon Jae Nick Nho). Submitted. arxiv:2306.04761
  7. Resolutions of toric subvarieties. by line bundles and applications. (with Andrew Hanlon, Oleg Lazarev). Forum of Mathematics, Pi
  8. Some cute applications of Lagrangian cobordisms towards examples in quantative symplectic geometry. (with Cheuk Yu Mak). Submitted. arXiv:2204.06432
  9. Realizability in tropical geometry and unobstructedness of Lagrangian submanifolds. To appear. Geometry and Topology
  10. Lagrangian cobordisms and Lagrangian surgery. Commentarii Mathematici Helvetici 98 no. 3
  11. Aspects of functoriality in HMS for toric varieties. (with Andrew Hanlon). Advances in Mathematics 401
  12. Observations on Disks with tropical Lagrangian boundary. MATRIX Annals 2019
  13. Wall-crossing from Lagrangian Cobordisms. Algebraic and Geometric Topology
  14. Tropical Lagrangian Hypersurfaces are Unobstructed. Journal of Topology 13
  15. Tropical Lagrangians in toric del-Pezzo surfaces. Selecta Mathematica 27
  16. Tropical Lagrangians and Homological Mirror Symmetry. PhD Thesis, UC Berkeley

Undergraduate Research Students

My reserach is funded by an EPSRC Open Fellowship.

Teaching and Outreach

  • Undergraduate teaching

    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.

  • Mentoring and Other Outreach

    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 run several 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.

    • Notes

  • Symplectic Snippets

    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)

  • Assorted Notes

    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!)

  • Seminars

    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

    • Positions

    Please feel free to contact me at anytime if you have questions about the possibility of working together.

  • PhD Position Fall 25

    I currently have a PhD position available with a starting date of Fall 2025 at the University of St Andrews. Please apply directly through their portal.

  • Postdoctoral Position Fall 26

    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.

  • PhD Position Fall 26

    I will have another PhD position available in Fall 26 - details to come!

    • Contact

  • Current Location

    office: 316 Mathematical Institute, St Andrews

    email:

    office hours: by appointment

  • Upcoming Locations

    Oberwolfach, Toric Geometry, 6 apr 2025

    Helmsley, Summer School on PW Fuk Cat., 13 jul 2025

    American Institute of Mathematics, HMS and MG Comm. Alg, 18 Aug 2025