Chris Xu

You can find me at HSS 3073 (UCSD).
Email: chx007(at)(school name)(dot)edu

About me

I am a 3rd year graduate student at UCSD, working under Kiran Kedlaya and Aaron Pollack. I expect to graduate in 2027. I'm interested in number theory, arithmetic geometry, Langlands program, homotopy theory and everything in between.
Here is my CV.

What I'm thinking about

• Almost all current methods for finding rational points on modular curves involve first finding a plane model before implementing quadratic Chabauty. With Kiran Kedlaya, I am currently developing a way to work directly with the moduli space without using any defining equations. Expect a draft to appear "soon".
• So far, quadratic Chabauty over number fields has only been made explicit for special cases (e.g. hyperelliptic or bielliptic). I am thinking about how to generalize the techniques in the "cursed curve paper" to number fields.
• With Aaron Pollack, I am investigating relations between cohomology classes of certain special cycles on the symmetric space associated to the split real form of G_2. Investigating these relations involves producing half-integral weight modular forms via theta lifting. Expect a draft to appear "soon".

Preprints

• On Skelet #17 and the determination of BB(5) (2024, rough draft, need to add references)

Teaching

• Winter 2024 (current): Math 20D
• Fall 2023: Math 20E
• Spring 2023: Math 20E
• Winter 2023: Math 20C
• Fall 2022: Math 20B
• Spring 2022: Math 106
• Winter 2022: Math 20C
• Fall 2021: Math 20B

Seminars

We have quite a few student-ran seminars each quarter. This quarter I am participating in:

• Prismatic F-gauges seminar (ran by Nathan Wenger)
• Lawrence-Venkatesh seminar (ran by Matt Broe)