Zhiyu Zhang

Service and Outreach

I grew up in a small rural town in Hunan, where there were essentially no educational resources. I am the first person in my family to attend college. I believe that math is for everyone. It is my responsibility to contribte to the community and make math accessible and enjoyable.
I welcome review invitations and have been reviewers for more than 8 mathematical journals.
I enjoy working with students from all backgrounds interested in number theory, algebraic geometry and representation theory.
I have mentered 7 undergraduates for their study and research, written 2 letters of recommendation and provided 1 research project, including direct reading programs at MIT and summer research at Stanford.
I mentered several MIT undergraduates to learn and explore mathematics e.g. applied category theory via MIT directed reading program (2019-2021).
I suggested a REU project in computing Gelfand-Kirillov dimension, see this paper.
I was a math coach of Tsinghua Mathcamp for high school students in Summer 2019.
I have given 1 public lecture in the Stanford math department for graduates and undergraduates, for the Faculty Area Research (FARS) seminar.
I have taught an undergraduate algebraic geometry micourse for an summer school on number theory, Beijing, Summer 2025.
I am the reporter for Arbeitsgemeinschaft: Relative Langlands Duality , March 2025.
I maintained the problem list for the AIM workshop arithmetic intersection theory on Shimura varieties .
I co-organized the Representation Theory Seminar at Stanford, Fall 2025.
I co-organized the Arithmetic Geometry Preprint Seminar (Fall 2023).
I co-organized Euler System Program Special Seminar with Ben Howard , Spring 2023.
I co-organized MIT STAGE Seminar (Spring 2020 -- Fall 2021) .
I organized a reading seminar on Rapoport--Zink spaces , Fall 2021.
I have submitted H&S Faculty Annual Report (2024), Stanford University.

Some seminars and courses at Stanford

Usual Tea time: 3:30 pm Weekdays (+ 5:30 pm Friday). See also Math Seminars at UC Berkeley.

Joint Berkeley-Stanford Algebraic Number Theory (Tuesday 2:30-4:30 pm). Topics we tried to learn:

  • Elliptic units for complex cubic fields, Fall 2025.
  • Igusa stacks, Winter 2025-Spring 2025.
  • Irrationality of zeta values (Calegari-Dimitrov-Tang), Fall 2024.
  • V. Pilloni's lectures on Pan's theorem that de Rham implies classicality for overconvergent modular forms, Spring 2024.
  • Perfectoid modular curve and the Hodge-Tate period map , Winter 2024.
  • Absolute Hodge and motivated cycles, Fall 2023.

    • Stanford Number Theory Seminar (Monday 2-3 pm, with lunch).

    Stanford Topology Seminar (Tuesday 4 pm).

    Stanford Algebraic Geometry Seminar .


    Below are some courses I find interesting at Stanford.

    Math 245A: Topics in Algebraic Geometry (Alterations), Brain Conrad, Winter 2025.

    MATH 249: Topics in Number Theory (proof of Fermat's Last Theorem and definite quaternion algebras over totally real fields) , Richard Taylor, Fall 2025.

    MATH 249C: Topics in Number Theory (Prismatic Dieudonne theory), Si Ying Lee, Spring 2025.

    MATH 245C: Topics in Algebraic Geometry (algebraic, combinatorial, and geometric ideas around modular representation theory), Calder Morton-Ferguson, Spring 2025.

    MATH 263B: Topics in Representation Theory (Depth zero affine Hecke category), Xinwen Zhu, Winter 2025.

    MATH 249B: Topics in Number Theory (Modular lifting theorems), Richard Taylor, Winter 2025.

    MATH 249A : Topics in Number Theory (Bruhat-Tits theory), Brain Conrad, Fall 2024.

    MATH 249B : Topics in Number Theory (Tame categorical local Langlands), Xinwen Zhu, Winter 2024.

    MATH 263A : Topics in Representation Theory (Solvable Lattice Models), Daniel Bump, Fall 2023.


    Below are some previous seminars at MIT.

    MIT Number Theory Seminar
    MIT Lie Groups Seminar
    Harvard–MIT Algebraic Geometry Seminar


    Time Schedule at Stanford

    2023: Fall (Sep 26-Dec 8).
    2024: Winter (Jan 8-Mar 15), Spring (Apr 1-June 5), Fall (Sep 23 - Dec 6).
    2025: Winter (Jan 6-Mar 14), Spring (Mar 31-June 4), Fall (Sep 22 - Dec 12).
    2026: Winter (Jan 5-Mar 22), Spring (Mar 30-June 10).

    Some notes

    Dehn twists, and full monodromy of Kodaira–Parshin families (2022), MIT STAGE seminar.
    Spherical varieties and L-functions (2021). MIT spherical variety learning seminar.
    Derived category of mixed complexes and Weil II (2021). Michigan BBDG seminar.
    Perfectoidization and perfect prismatic complex (2021). MIT STAGE seminar.
    The Drinfeld half plane (2021).
    Galois category and Riemann existence theorem (2021). Princeton Exodromy seminar.
    Frobenius on p-adic modular forms and the theta operator (2020). MIT STAGE seminar.
    Weight spectral sequence and Weil conjecture (2020). MIT STAGE seminar.
    p-divisible groups and Hodge structures (2019). MIT STAGE seminar.
    A rough introduction to Lubin-Tate spaces (2018).