Jae Hee Lee
Department of Mathematics
E-mail address: jaehelee at mit dot edu (this is not a typo, the username is missing an 'e' from my name)
Hello! I am a second year graduate student at MIT. I'm interested in symplectic topology, or more broadly in mathematics near the interface between mathematics and physics. My advisor is Paul Seidel.
My Curriculum Vitae. (Last Update: Jan 2022)
Quantum Steenrod Operations
My current project is about quantum Steenrod operations, which are endomorphisms of the equivariant quantum cohomology algebra over finite fields. These operations are defined from equivariant counts of genus 0 J-holomorphic curves in symplectic manifolds. I am developing methods to compute these operations in the range of degrees where they are no longer determined by ordinary Gromov--Witten invariants and classical Steenrod operations. This is the range where contributions from p-fold covers become relevant, and also the range that is beyond the reach of the current methods to compute these operations.
Double Ramification Contact Homology
For my undergraduate honors thesis, I worked on a modification of contact homology as defined by Eliashberg--Givental--Hofer that incorporates the Hodge classes from the moduli space of stable curves. The construction is motivated by quantum integrable hierarchies known as the double ramification hierarchy, as studied by Buryak--Rossi. A draft is available at request.
Seminars and Workshops
In Summer 2022, I co-organized Kylerec 2022. The topic was quantitative symplectic geometry.
In Spring 2022, I co-organized a Reading group on Ganatra--Pardon--Shende I, II with Zihong Chen.
These are some expository notes I have written. I would greatly appreciate if you could let me know of anything incorrect or misleading.
Atiyah--Bott localization theorem UChicago REU 2019
String Topology MIT Kan Seminar IAP 2021
Brief Intro to Spectra MIT Informal Symplectic Seminar 2021
Quantization of free field theories, following Costello--Gwilliam MIT Juvitop Fall 2021
Quantum cohomology of flag varieties Harvard Universal Centralizers Seminar 2021