Emails: zyuzhang[at]stanford.edu / zhiyuzhangmath[at]gmail.com .

Postdoctoral researcher (Spring 2023, Simons Laufer Mathematical Sciences Institute).

PHD (2018-2022, MIT) under the supervision of Wei Zhang (and Zhiwei Yun).

Undergraduate (2014-2018, Tsinghua), visiting École normale supérieure (Spring 2018).

Currently I enjoy thinking about

I hope to formulate new conjectures and geometric objects (based on new examples) and prove new theorems (there are still many exciting things to be further explored). I enjoy the compatibility of pictures over p-adic numbers, real numbers, rational numbers and topology (e.g. from local systems on 3-manifolds and physics).

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--MATH 216B, Graduate Algebraic Geometry, Winter 2025.

MATH 216A Graduate Algebraic Geometry, Fall 2024, TuTh 12:00-01:20 PM, Room 381T. Website .

MATH 263A Topics in Representation Theory, Function Field Arithmetic, Fall 2024, TuTh 10:30-11:50 AM, Room 381T. Website (under construction).

MATH 145 Algebraic Geometry, Spring 2024, MWF 9:30-10:20 AM. Website .

MATH 263C Topics in Representation Theory, Relative Langlands duality, Spring 2024, MWF 10:30-11:20 PM. Website .

Previous teaching at MIT: Recitation Instructor for 18.06 Linear Algebra (Fall 2021). Teaching Assistant for 18.726 Algebraic Geometry II, 18.706 Algebra II (Spring 2022), 18.786 Number Theory II, 18.737 Algebraic Groups (Spring 2021), 18.785 Number Theory I (Fall 2020), 18.102 Introduction to Functional Analysis (Spring 2020), 18.705 Commutative Algebra (Fall 2019).

I enjoy working with students from all backgrounds interested in number theory, algebraic geometry and representation theory. We could begin a discussion by e-mail.

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

Stanford Topology Seminar (Tuesday 4 pm).

Stanford Algebraic Geometry Seminar (Friday 11:30 am).

Joint Berkeley-Stanford Algebraic Number Theory (Tuesday 2:30-4:30 pm).

Math Seminars at UC Berkeley.

Stanford Tea time: 3:30 pm Weekdays (+ 5:30 pm Friday).

Math 269 TuTh (1:30-2:50 pm), Spring 2024. MIT Number Theory Seminar

MIT Lie Groups Seminar

I co-organized the Arithmetic Geometry Preprint Seminar (Thursday 2:00-3:30 pm).

I maintain the problem list for the AIM workshop arithmetic intersection theory on Shimura varieties .

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 mentered several MIT undergraduates to learn and explore mathematics e.g. applied category theory via MIT directed reading program (2019-2021).

I was a math coach of Tsinghua Mathcamp for high school students in Summer 2019.

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).

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).

Overleaf

MacTutor

Mathscinet (AMS remote access available)

Stacks Project

The Automorphic Project

Kerodon, an online resource for homotopy-coherent mathematics

Mathematics Genealogy Project

Mathoverflow (see e.g. helpful answers of P. Scholze, W. Sawin, D. Loeffler and other people)

Mathjobs

Conferences in arithmetic geometry

quiver: a modern commutative diagram editor

LMFDB - The L-functions and modular forms database

Numdam, the French digital mathematics library

American Mathematical Society

European Mathematical Society

Mathematisches Forschungsinstitut Oberwolfach

African Institute for Mathematical Sciences

IAS/Park City Mathematics Institute

Institute of the Mathematical Sciences of the Americas

International Mathematical Olympiad

The University of Chicago Mathematics REU

Essential Number Theory

ICM 2026 in Philadelphia, USA

Virtual ICM 2022

Equipe Formes Automorphes, IMJ-PRG

PU/IAS Number Theory Seminar

Harvard Number Theory Seminar

Number Theory Web Seminar

UCSD Number Theory Seminar

Johns Hopkins Number Theory Seminar

Johns Hopkins University & University of Maryland Algebra and Number Theory Day

MIT Juvitop Seminar

Boston College NT/RT Seminar

Boston University Number Theory Seminar

Weekly seminars at Columbia University

Events and Activities | Institute for Advanced Study

M2 "Mathématiques fondamentales"

Caltech Number Theory Seminar

UCLA Number Theory Seminar

Number Theory / Representation Theory Seminar, University of Wisconsin - Madison

Mathematical Events in Bonn

Arithmetic Geometry and Representation Theory in Münster

Seminar "Algebra and Number Theory" at University of Vienna

International Seminar on Automorphic Forms, TU Darmstadt

Upcoming conferences in algebraic geometry by Ravi Vakil

Conferences in arithmetic geometry by Kiran Kedlaya

Geometric Langlands page by David Ben-Zvi

Between electric-magnetic duality and the Langlands program by David Ben-Zvi

Suggestions for mathematical writing and speaking by Bjorn Poonen

Finding your path by Rahul Pandharipande

Selected Articles on mathematicians by Allyn Jackson

The work of Robert Langlands by James G. Arthur

Cohomology of Arithmetic Groups by Günter Harder

Towards a theory of local Shimura varieties by Michael Rapoport, Eva Viehmann

Towards a Jacquet-Langlands correspondence for unitary Shimura varieties David Helm

On the Shafarevich and Tate conjectures for hyperkähler varieties by Yves André

Maass cusp forms with integer coefficients by Peter Sarnak

Lecture notes on Hodge theory by Phillip Griffiths

Lecture notes on derived algebraic geometry / algebraic stacks by Adeel A. Khan

Lecture notes on modularity lifting theorems by Toby Gee

Lecture notes on stacks and moduli by Jarod Alper

Arizona Winter School 2022 Lectures by Akshay Venkatesh

RAMpAGe Seminar

Kolyvagin's work on modular elliptic curves by Benedict H Gross

Foliations in Moduli Spaces of Abelian Varieties and Dimension of Leaves by Frans Oort

Values of Zeta Functions and Their Applications by Don Zagier

The arithmetic and topology of differential equations by Don Zagier

Elliptic Modular Forms and Their Applications by Don Zagier

Lecture notes on perfectoid Shimura varieties by Ana Caraiani

Lattices and L-functions from nothing by Andrew V. Sutherland

Tannaka Reconstruction and Quasi-Coherent Stacks, Representability Theorems in Spectral Algebraic Geometry by Jacob Lurie

Model Theory and Differential Equations by Joel Nagloo

Derivatives of Eisenstein series and Faltings heights by S. Kudla, M. Rapoport, T. Yang. Modular Functions and Special Cycles by Maryna Viazovska

Selected talks by A. Okounkov

Survey on Some perspectives on Eisenstein series by Erez Lapid

Survey on Derived Symplectic Geometry by Damien Calaque

Survey on Algebraic Dilatations by Adrien Dubouloz, Arnaud Mayeux and João Pedro dos Santos

Survey on Affine Hecke Algebras and their representations by Maarten Solleveld

Survey on p-adic L-functions by Joaquín Rodrigues Jacinto and Chris Williams

ICM address On the Brumer-Stark Conjecture and Refinements by Samit Dasgupta and Mahesh Kakde

ICM address Topological Field Theory, Higher Categories, and Their Applications by Anton Kapustin

ICM address Categorification: tangle invariants and TQFTs by Catharina Stroppel

ICM address The distribution of values of zeta and L-functions by Kannan Soundararajan

ICM address No Where to Go But High: A Perspective on High Dimensional Expanders by Roy Gotlib and Tali Kaufman

ICM address Cohomology of Arithmetic Groups by Akshay Venkatesh

ICM address Statistics of Number Fields and Function Fields by Akshay Venkatesh and Jordan S. Ellenberg

ICM address Hecke algebras and harmonic analysis by Eric Opdam

Youtube Math Channel Institut des Hautes Études Scientifiques (IHÉS)

Youtube Math Channel 3Blue1Brown for everyone

A TED talk on procrastination

A page on Most cited mathematicians

I believe that computers are able to help humans with proofs, computations and finding mathematical patterns. See also the talk by Michael R. Douglas at Western Hemisphere Colloquium on Geometry and Physics.

I am interested in increasing accessibility and descreasing language barriers in mathematics. I helped with Chinese translation in Visual Mathematical Dictionary project. I could also help translate math papers in Japanese and French.

The Banana Space is an online mathematics wiki in Chinese, similar to the nLab .

I am interested in connections between mathematics and arts. See works of Maurits Escher and Journal of Mathematics and the Arts . I did some mathematical paintings.

I am interested in serious recreational mathematics. I enjoy logic puzzles and puzzle games. With some people I made a free translation of the puzzle game Bean and Nothingness , designed by math PHDs from University of Michigan. I also enjoy math jokes, see for instance My Favorite Math Jokes by Tanya Khovanova.

I was the main editor of the student journal He Si during 2017-2018.

I won the gold medal in the overall part of Yau College Student Mathematics Contest in 2017.

I was a volunteer for Strings 2016 Conference in Beijing.

For me, doing math is a life-long Odyssey (see also A Mathematical Odyssey ). I also enjoy traveling (thinking and doing math along the way). I have been to more than 20 countries.