Research

I am interested in local and global aspects of automorphic representations and Langlands program, especially period integrals and automorphic generating functions.
I am studying cycles and correspondences on revelant moduli spaces (e.g. Shimura varieties) and many different roles they play.
In particular, I am studying related intersection numbers, p-adic geometry and cohomology at general levels (beyond special parahorics) via geometric and automorphic tools.

1. Maximal parahoric arithmetic transfers, resolutions and modularity. Arxiv:2112.11994. Submitted.
   Talks:
   • Modularity and Bruhat--Tits stratification, University of Arizona Algebra and Number Theory Seminar, April 5.
   • Singularity and arithmetic transfers at parahoric levels, Yale Algebra and Number Theory Seminar, April 19.
   • Modularity and geometry of Shimura varieties at parahoric levels, Boston College NT/AG Seminar 2021-22, April 21.
2. In preparation.
   Talks:
   • Arithmetic modularity and geometry of Shimura variety at parahoric levels, University of Maryland, May 19.
   • Arithmetic transfer identites and singularities at parahoric levels, University of Maryland, May 20.
3. ..
   

I am also keep learning more about parahorics, representation theory, p-adic geometry and algebraic topology via reading (recent) papers.
Here is a partial reading/reference list (orderd roughly by time, with a up to date version available).

Teaching

Teaching Assistant for 18.705, Commutative Algebra, Fall 2019.
Teaching Assistant for 18.102, Introduction to Functional Analysis, Spring 2020.
Teaching Assistant for 18.785, Number Theory I, Fall 2020.
Teaching Assistant for 18.737, Algebraic Groups, Spring 2021.
Teaching Assistant for 18.786, Number Theory II, Spring 2021.
Recitation Instructor for 18.06, Linear Algebra, Fall 2021.
Teaching Assistant for 18.706, Algebra II, Spring 2022.
Teaching Assistant for 18.726, Algebraic Geometry II, Spring 2022.
DRP I mentored two undergraduates on reading:
Fundamental Algebraic Geometry: Grothendieck’s FGA Explained, January 2019.
Categories for the Working Mathematician, and chapter 1 of Kerodon, January 2020.
The 1-2-3 of modular forms, and additional material on singular moduli, January 2021.

Seminars

MIT STAGE Seminar:

Spring 2022: Uniform Mordell II.

Fall 2021: Uniform Mordell. (co-organizer).

Spring 2021: Crystalline cohomology and prismatic cohomology (co-organizer).

Fall 2020: The Weil conjectures (co-organizer).

Spring 2020: p-adic modular forms (co-organizer).

Fall 2019: Formal groups and p-divisible groups.

Rapoport--Zink spaces , Fall 2021.
Berkeley Notes, Summer 2021.
MIT Juvitop Seminar, Spring 2021
Condensed Math Seminar Spring 2021, with Longke Tang, Yixiao Li. Notes (Chinese) .
Seminar on spherical varieties (Spring 2019).

Notes and Slides

• A rough introduction to Lubin-Tate spaces
• Matching and orbital integrals (Jacquet-Rallis case)
• Intersecting CM cycles and KR divisors
• Scholze-Weinstein's classification of p-divisible groups
• Learning note on (ultra) Weil II
• (Extended slides) Frobenius on p-adic modular forms and the theta operator
• (Extended slides) Weight spectral sequence and Weil conjecture by deformation
• Rough notes on the geometrization course in Bonn (Fall 2020):
  1030 , 1102 , 1106 , 1109 , 1113 , 1116 , 1120 , 1123 , 1127 , 1130 , 1204 , 1207 , 1211 ,
  1214 , 1218 , 1221 , 0108 , 0111 , 0115 , 0118 , 0122 , 0125 , 0129 , 0201 , 0205 , 0208 , 0212 .
• Fixed point locus on p-adic half plane
• (Extended slides) Spherical varieties and L-functions
• (Slides) Galois category and Riemann existence theorem
• (Slides) Galois action on KSp and on CM abelian varieties
• (Slides) Derived category of mixed complexes and Weil II
• (Slides) Perfectoidization and perfect prismatic complex
• (Rough notes) Dehn twists, and full monodromy of Kodaira–Parshin families

Miscellaneous (non-math)

In my spare time, I play and do puzzle game designs. Recently I with some people made a free translation of Bean and Nothingness , designed by math PHDs from University of Michigan.

Last updated: May 25, 2022. Next: June 2 2022.