Jeff Hicks

I'm an EPSRC postdoctoral fellow at the University of Edinburgh, working with Nick Sheridan. I grew up in Cardiff-by-the-Sea, California before getting my MA at UCLA. At UC Berkeley I received my PhD under the supervision of 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

Tropical Lagrangians and 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. The Lagrangian lift of a tropical subvariety gives a hands on approach to homological mirror symmetry. I'm currently looking into methods for computing the open Gromov-Witten invariants of these Lagrangian submanifolds with a goal of relating realizability of a tropical curve to unobstructability of the Lagrangian submanifold lift.

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.

Publications and preprints

Reverse isoperimetric ineq. for Lag. int. Floer th. (with J.-P. Chassé, Y.J. Nho). arxiv:2306.04761
Resolutions of toric subvar. by line bundles and app. (with A. Hanlon, O. Lazarev). arXiv:2303.03763
Some cute app. of Lag. cob. towards examples in quant. symp. geo. (with Cheuk Yu Mak). arXiv:2204.06432
Tropical Realization criteria from symplectic geometry. Submitted. arXiv:2204.06432
Lagrangian cobordisms and Lagrangian surgery. Accepted. Commentarii Mathematici Helvetici
Aspects of functoriality in HMS for toric varieties. (with Andrew Hanlon). Adv. in Math. 401
Observations on Disks with tropical Lagrangian boundary. MATRIX Annals 2019
Wall-crossing from Lagrangian Cobordisms. To appear. Algebraic Geometry and Topology
Tropical Lagrangian Hypersurfaces are Unobstructed. Journal of Topology 13
Tropical Lagrangians in toric del-Pezzo surfaces. Selecta Mathematica 27
Tropical Lagrangians and Homological Mirror Symmetry. PhD Thesis, UC Berkeley

Teaching and Outreach

Teaching at University of Edinburgh

I'm not currently teaching at University of Edinburgh. Previously, I ran tutorial sessions for Several Variable Calculus and Differential Equations and cotaught "Interactions in Algebra, Geometry, and Topology".

Teaching at University of Cambridge

I've been an ASCR with Kings College, where I supervised students in analysis and algebraic topology. I've additionally helped out with examples courses for symplectic geometry.

Teaching at UC Berkeley

At UC Berkeley, I have been supported by both GSI, GSR and teaching fellowship funding. Courses include second semester calculus in Fall 13; Linear algebra in Spring 14 ; and Multivariable calculus in Fall 14 , Spring 16 , and Fall 17 . I was also the instructor for Math 32 in Spring 19. In addition to my GSI work, I've taught and developed course material for an undergraduate topics and introductory research course during Spring 15 and 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.

Outside of Berkeley's DRP program, I've run a summer research project for undergraduates:

Daniel Holmes. Affine dimers from characteristic polygons. PUMP J. of Undergrad. Res.

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

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

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

Seminar Notes

Here are a few notes I've put together for seminar talks I've given. As these are seminar notes assembled primarily for my own benefit, they are all in draft form, and all mathematical errors are my own.

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)

Exposition on Family Floer Theory (HMSS 2018)

Continuation map for the Fukaya Morse Algebra (HMSS 2018)

Polyfolds School (Summer 2017)

Graph Cohomology and Perturbative Methods(STQFTS 2016)

Classical Mirror Symmetry (SSS 2016)

Stability Structures for Categories (MSS 2016)

Sheaf-approaches to the Fukaya Category (MSS 2016)

Knot Contact Homology (SDGT, 2016)