Ongoing
Together with Kiran S. Kedlaya and Jun Bo Lau, we are making an effort to make a census of genus 7 curves over F2. Please contact one of us for a status update.
Preprints
A census of genus 6 curves over F2 (with Kiran S. Kedlaya and Jun Bo Lau), 2024. (repo)
Research Talks
April 2025: Census of genus 6 curves over F2 (UCSD Number Theory Seminar)
July 2024: Census of genus 6 curves over F2 (ANTS XVI) Lightning Talk (5 minutes) slides
July 2023: Model-free Chabauty-Coleman integration on modular curves (LuCaNT) Lightning Talk (5 minutes)
Workshops/Conferences Attended
Annual Meeting of the Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation - January 15-16; NYC, NY
ANTS XVI - July 15-19, 2024; MIT, Cambridge, MA.
The Mordell conjecture 100 years later - July 8-12, 2024; MIT, Cambridge, MA.
Hypergeometric Motives in the LMFDB - April 22-26, 2024; MIT, Cambridge, MA.
Modular Curves in the LMFDB III - March 11-15, 2024; MIT, Cambridge, MA.
Arizona Winter School 2024: Abelian Varieties - March 2-6, 2024; University of Arizona, Tucson, AZ.
Shimura Curves in the LMFDB - February 5-9, 2024; Dartmouth College, Hanover, NH.
LMFDB, Computation, and Number Theory (LuCaNT) - July 10-14, 2023; ICERM, Providence, RI.
Arizona Winter Semester 2021 - Spring 2021; online.
Connecticut Summer School in Number Theory (CTNT) - June 8-14, 2020; online.
Learning Seminars
Winter 2024: Diophantine problems after Lawrence-Venkatesh.
Fall 2023: Mazur's Torsion theorems
Summer I 2023: Étale cohomology, class field theory
Winter 2023: Faltings's proof of Mordell's Conjecture
Spring 2022: Class Field Theory (BUNTES)
Fall 2021: Shimura Varieties (BUNTES)
Expository Talks
2 talks series: Introduction to algebraic De Rham cohomology, Gauss-Manin connection, and crystalline cohomology (January 2024).
Definition and properties of etale cohomology: given at learning seminar on etale cohomology (July 2023)
Introduction to etale cohomology and etale morphisms: given at the learning seminar on etale cohomology (May 2023).
Adic spaces: given at the learning seminar on Fargues-Fontaine curves (April 2023).
Faltings's Isogeny Theorem: given at the learning seminar on Faltings's proof of Mordell's Conjecture (March 2023).
Group (co)homology: given in MATH 204B (UCSD Winter 2023) as part of a student-run learning seminar on group cohomology in preparation of the proof of local class field theory.
Solving equations? Not so easy (video): eight-minute overview of my undergradauate thesis presented at the 9th Kilachand Honors College Keystone symposium.
L-functions: given in BUNTES: CFT (Spring 2022).
Towards defining Shimura Varieties & Definition of Shimura Varieties: two separate talks given in BUNTES: Shimura Varieties (Fall 2021).
Geometry and arithmetic of elliptic curves: three-talk series given at counselor seminars during PROMYS 2021.
Introduction to commutative algebra and algebraic geometry: Eight-talk series given at counselor seminars during PROMYS 2020 (five given myself, one given by Alexandar Rodriguez, and two given by Wojtek Wawrów).
Note: Since these notes are written as a crucial part of my learning process, they may very well contain some (if not many) mistakes. Please use them at your own risk. You are welcome to point out any nontrivial mathematical errors in these notes to me.