# Chris Xu

You can find me at HSS 3073.

Email: chx007(at)(four letter school name)(dot)edu

Here is a photo of me at the Mordell conference (center-left, with the UCSD shirt). Here is another photo of me at the ANTS XVI conference the following week (center-right).

## About me

As of Fall 2024, I am a 4th year graduate student at University of California San Diego. I work in algebraic number theory. Currently I have Kiran Kedlaya and Aaron Pollack as advisors. I expect to graduate in 2027.

Here is my CV.

## What I'm thinking about

- Model-free Chabauty-Coleman on modular curves.
- Special cycles on G
_{2}.

## What I want to think about soon

*Please contact me if you are interested in any of these ideas.*
- Model-free (geometric) quadratic Chabauty.
- Explicit motivic Chabauty-Kim (after D. Corwin, N. Kantor).
- Serre uniformity in the non-split Cartan case.
- p-adic Gross-Zagier formula in the non-split Cartan case.
- Modular forms and modular symbols on G
_{2}.
- Dehn invariant 0 tetrahedra.

## Papers

- Period integrals on G
_{2}, *in progress*
- Chabauty on modular curves via the moduli interpretation (with Y. Huang, J. Lau, and I. Rendell),
*in progress*
- Skelet #17 and the fifth Busy Beaver number,
*preprint*

## Notes (TBA)

*Please contact me if you would like to see these notes written up, or if you have any suggestions.*
- Galois cohomology
- Spectral sequences
- Complex multiplication
- Chabauty-Kim

## Teaching

- Fall 2024 (current): Math 104/105
- Summer 2024: Math 20E
- Spring 2024: Math 20E
- Winter 2024: 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

### Federico Ardila's axioms

- Mathematical potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
- Everyone can have joyful, meaningful, and empowering mathematical experiences.
- Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
- Every student deserves to be treated with dignity and respect.

*Last updated: September 14th, 2024*