About me

I am currently a member at IAS. Starting from Fall 2025 I will be a postdoc at University of Michigan.

I earned my PhD from the University of Chicago in June 2023, under the supervision of Prof. Ngô, Bảo Châu. My legal name (Xiāo) is hard to pronounce for a typical English speaker, so I go by the name of Griffin. My research interest lies in the junction between representation theory, algebraic geometry and number theory. Mostly Langlands stuff.

Academics

Current research involves multiplicative Hitchin fibration and (twisted) endoscopy theory. I am trying to provide a unified proof of the fundamental lemmas in endoscopy theory (from standard to the yet unproven twisted weighted version) directly at group level.
The first stage of this project is the standard fundamental lemma for spherical Hecke algebras, whose Lie algebras analogue was originally proved by my PhD advisor. This stage is now complete (see Publications).
- Caveat: my thesis may be found on ProQuest, which essentially contains a 9075 percent complete version of the said project. However, I do not recommend checking it out due to numerous additions, changes, improvements and (most importantly) corrections since then.
The second stage involves two directions: stability of multiplicative Higgs bundles, and the analogues for the twisted adjoint action. Both are ongoing projects.
I am also interested in the broader relative Langlands program, especially the recent framework of Ben-Zvi–Sakellaridis–Venkatesh.
Qualification Topic A summary of Godement–Jacquet theory. A full note can be found here.

Publications

Multiplicative Hitchin Fibration and Fundamental Lemma (current, arXiv)
With Zhiyu Zhang: Relative Fundamental Lemmas for Spherical Hecke Algebras and Multiplicative Hitchin Fibrations: the Jacquet–Rallis Case (arXiv)

Notes

A summary of Langlands and Shelstad’s paper on the definition of endoscopic transfer factors. There are minor typos found, but I am too lazy to update it now since it is now incorporated in my fundamental lemma paper as an appendix.
A note on Harder-Narasimhan filtration for reductive groups. This is the note of my talk at the BunG Seminar at the University of Chicago in Winter 2023.
These notes were written when I was a bigger idiot than I am now. So use at your own risk.
- A short note on p-adic integrals in algebraic setting.
- A tiny 3-page note recorded during Ngô’s seminar explaining the most basic part of the Hitchin fibrations, which I (at the time) found both concise and conceptually satisfying.
- (~~Possibly~~Definitely forever) unfinished notes for V. Ginzburg’s class Geometric Satake in Spring 2018.

Teachings

2022–2023 MATH 15200 (Calculus II)
2021–2022 MATH 15300 (Calculus III)
2020–2021 MATH 15200/15300 (Calculus II/III)
2019–2020 MATH 15100/15200/15300 (Calculus I–III)
2018–2019 MATH 15100/15200/15300 (Calculus I–III)
2017–2018 (TA) MATH 16110/16210/16310 (Honor Calculus IBL)

Misc.

CV
I have become a Nazgûl, and ever been a servant for carrying out my Lord Sauron’s Schemes, particularly the Final Object: the One Ring to rule us all.
I am a game addict.
- Some games I have been ~~wasting hundreds of hours on~~ enjoying
  - math (currently a professional player)
  - The Legend of Zelda Breath of the Wild (I found all 900 Korok seeds and completed Trial of the Sword in Master Mode without using glitch :)
  - The Legend of Zelda Tears of the Kingdom (I wish I could glue my own hovering bike)
  - Fire Emblem Three Houses and Fire Emblem Engage
I delivered a lecture about competitive Pokémon battle at the University of Chicago during my teaching training.
I also conduct some casual research in knot theory, during which I found a broken link (now removed) on Jon DeWitt’s page.
Pretentious meaning behind my logo
The name Griffin comes from the mythological creature griffin (or gryphon, or griffon). My first name means "courage", and my last name means "king" (which is nothing special since 99% of the Chinese are descendants of a handful of ancient rulers; probably also true for other civilizations if I have to guess), both of which a griffin heraldically befits. The logo is my own design. It is a deformation of the Chinese characters for my name "驍(Xiāo)王(Wáng)" into a Griffin.