# Math

I am broadly interested in geometric representation theory. I am fortunate to be advised by Roman Bezrukavnikov and Mihnea Popa.

## Talks in learning seminars

Here are some talks I gave for learning seminars, listed roughly in reverse chronological order. Sometimes I wrote notes for them, in which case they’ll be posted below.

- In April 2024, I gave two talks on stability conditions on quiver representations for the Bridgeland stability learning seminar; the notes are linked below.
- In April 2024, I gave a pre-talk on Springer fibers for the Harvard-MIT Algebraic Geometry Seminar; the notes are linked below.
- In Spring 2024, I’m running a learning seminar on the book Representation Theory and Complex Geometry. More details can be found here.
- In February 2024, I gave a talk on the McKay correspondence and categorification of root systems for Harvard’s Trivial Notions seminar.
- In February 2024, I gave a talk on D-modules on stacks for the GL Support Group seminar. The notes can be found on the seminar page and are also linked below.
- In November 2023, I gave two talks on deformation theory via differential graded Lie algebras for a deformation theory learning seminar at Harvard; notes are linked below.
- In October 2023, I gave two talks on derived categories for the Bridgeland stability learning seminar at Harvard; notes are linked below.
- In Summer 2022, I helped run Chroma, a learning seminar on stable and chromatic homotopy theory.
- In February 2022, I gave a talk on GIT quotients and moduli spaces at the MIT Directed Reading Program Symposium.

## Notes

Here are some notes I wrote, listed roughly in reverse chronological order. Please let me know if you find any errors!

- I was reading about D-modules and wrote a summary of the results, with emphasis on the functorial formalism for holonomic D-modules.
- I gave two talks on stability conditions on quiver representations for a learning seminar on Bridgeland stability.
- I gave a pre-talk for the Harvard-MIT Algebraic Geometry Seminar on Springer fibers. These notes are a (fairly significantly) expanded version of that talk.
- Hunter Dinkins gave me a nice perspective on Hopf algebras. These notes are meant to summarize my understanding of the motivation for defining Hopf algebras; the goal is to explain why Hopf algebras are actually a very natural construction, despite its seemingly unwieldly definition.
- I gave many talks for the Chriss-Ginsburg Learning Seminar, and some notes are attached there.
- I gave a talk for the Geometric Langlands Support Group seminar, D-modules on stacks.
- While reading chapter V.5 of Hartshorne, I wrote notes summarizing the content: Birational maps.
- I helped write the notes for the class 18.706, Noncommutative Algebra, along with Serina Hu, Vasily Krylov, and Roman Bezrukavnikov.
- I took notes for the class 18.747, Infinite-dimensional Lie algebras. The professor was Leonid Rybnikov, and it was taught at MIT in Fall 2023.
- I gave two talks on derived categories for a learning seminar on Bridgeland stability.
- I gave two talks on differential graded Lie algebras and deformation theory for a learning seminar on deformation theory.
- While reading about the Sato-Kashiwara filtration, I wrote notes summarizing what I learned.
- I took a communications in mathematics class, 18.784, in Fall 2021 as an undergrad at MIT. For this class, I wrote an expository paper on Chevalley groups, Bruhat-Tits apartments, and Moy-Prasad filtrations.