About me

I am currently a member at IAS during academic year 2023–2024. Starting from Autumn 2024 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) directly at group level.
The first stage of this project is the standard fundamental lemma for spherical Hecke algebras, originally proved by my advisor for Lie algebras. This stage is close to completion, and I plan to release a draft soon in two or three parts.
- My thesis may be found on ProQuest, which essentially contains a 90 percent completion version of the said project. However, I do not recommend checking it out right now due to numerous changes, improvements and corrections since then.
- All the major technical difficulties listed in my thesis have now been overcome, so reading that version will likely cause some unnecessary confusion.
- There have been several important errors found, and mostly fixed at this point. Some of them were due to my lack of understanding of the materials when I wrote the relevant part, while some were (as my excuse) due to the crunch to catch the graduation deadline.
Qualification Topic A summary of Godement-Jacquet theory. A full note can be found here.
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 likely to be 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. A minor error was pointed out to me and I will update the note (with due credit) when I have more time.

Other Notes

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’m a gamer.
- The 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 (ongoing)
  - 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 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.