I am a Szegő Assistant Professor at Stanford University. I am on job market for positions starting at Fall 2026.
I did my PHD (2018-2022) at MIT, where my advisor was Wei Zhang (-Zhang-Szpiro-Samuel/Auslander-...).
I work in number theory, representation theory and arithmetic geometry of moduli spaces. I am trying to do more computations, fully understand some fundamental open questions and find new phenomenons, see more on Research page. They include:
How to understand automorphic periods in relative Langlands? Complete solutions will advance arithmetic / categorical analogs.
How do you understand cycles on moduli spaces via Langlands program, e.g. non-vanishing, volumes, Selmer groups and L-functions? Examples: (twisted) AFL, (mixed) theta liftings, Kudla program and arithmetic level raising. To match B-side and arithmetic, we need more non-reductive linear algebra and cycles. Sometimes number field may be better than function field, see e.g. arithmetic twisted GGP conjecture.
How to use (classical limits of) spectral / geometric Langlands machine to do arithmetic over Q, via local fields? Since Ngô's proof of endoscopic fundamental lemma (ABCDEFG), we study Dolbeault moduli of Higgs bundles for tricky (arithmetic) haramonic analysis questions.
How do you understand (arithmetic) 1-cycles in Shimura varieties? It is related to motivic local systems (or Hodge structures) on curves, exceptional reductions, Shafarevich hyperbolicity and arithmetic relative Langlands (via derived zeros of special functions).
Do we fully understand unitary / orthogonal Shimura varieties, arithmetic GGP conjecture and Kudla program, e.g. ramification and blow ups? We are trying to complete these programs for many applications, similar to current trends on arithmetic statistics, full rank one BSD and modularity of elliptic curves. The story on curves (resp. 3-folds) is mostly completed (resp. to-be-done).
I enjoy teaching, talking about math, working with people and contributing to the community.
Email: zyuzhang[at]stanford.edu / zhiyuzhangmath[at]gmail.com .
Office: Room 382-C, Sloan Mathematical Center.
PHD thesis on a global method to prove arithmetic transfers and modularity of arithmetic theta series, allowing ramifications and blow ups, with applications to Bloch-Kato conjecture on Shimura varieties, see e.g. lecture notes (C. Li, W. Zhang) of IHES 2022 summer school on Langlands program.
Undergraduate thesis on Merkurjev-Suslin theorem, Tsinghua University / ENS Paris, Spring 2018.
News (see Talks / Travels ) :
(2025/11)
(2025/10)
(2025/9)
(2025/8)
(2025/8) Teaching algebraic geometry, undergraduate summer school on number theory, Beijing.
(2025/7)
(2025/7)
(2025/6)
(2025/6)
(2025/5)
(2025/5) Conference Talk at 37th Automorphic
Forms Workshop .
(2025/4) A new paper On unitary Shimura varieties at ramified primes. (with Yu Luo and Andreas Mihatsch).
(2025/4) Colloquium talk on programs around L-functions, non-reductive cycles and more questions at Rutgers University.
(2025/4) Research talk on non-reductive periods and L-functions at University of Michigan.
(2025/4) A new paper on Weighted cycles on Rapoport--Zink spaces with almost-self dual level structure. (with Qiao He and Baiqing Zhu).
(2025/3) Reporter for Arbeitsgemeinschaft: Relative Langlands Duality .
(2025/2) Seminar Talk on Anti-spherical quotient and Iwahori-Whittaker category (Arkhipov-Bezrukavnikov Equivalence), Geometric representation theory Seminar, Stanford.
(2025/2) A new paper on Non-reductive cycles and twisted arithmetic transfers for Shimura curves .
(2025/1) Conference Talk on Arithmetic aspects of automorphic forms and automorphic representations , Kyoto University.
(2025/1) Teaching MATH 145 (MWF 01:30 PM - 02:20 PM) and MATH 216B (MWF 10:30 AM - 11:20 AM) on Algebraic Geometry (based on the rising sea, stacks project and Hartshorne's book).
(2024/12) Visiting MIT, Boston.
(2024/11) Research talk at POSTECH-PMI Number Theory Seminar , Korea.
(2024/10) Attending Oberwolfach Seminar: Reduction of Arithmetic Varieties .
(2024/9) Teaching a topic course on Function Field Arithmetic focusing on type A, and a algebraic geometry course focusing on quasi-coherent sheaves (as linearizations / spaces of states).
(2024/8) A new paper with X. Griffin Wang on spherical relative Fundamental Lemmas .
(2024/7) Conference talk at BIRS workshop Branching Problems for Representations of Real, p-Adic and Adelic Groups , Kelowna, Canada.
(2024/6) A new paper on Non-reductive special cycles and twisted arithmetic fudamental lemmas (inspired by relative Langlands program).
(2024/6) Conference Talk at Simons Symposium: Periods and L-values of Motives (2024), Krün, Germany.
(2024/4) Research talk at Stanford Number Theory seminar.
(2024/4) Conference talk at the AMS Sectional Meetings , Howard University, Washington, DC.
(2024/3) Senior participant of Arizona Winter School 2024: Abelian Varieties.
(2024/3) Teaching MATH 263C Topics in Representation Theory: Relative Langlands duality, and MATH 145 Algebraic Geometry.
(2024/2) Research talk at Number Theory / Representation Theory Seminar, University of Wisconsin - Madison .
(2024/1) Problem list for the AIM workshop arithmetic intersection theory on Shimura varieties.