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Hao Peng

I am a graudate student at department of mathematics, MIT, starting from Fall 2021. My advisor is Wei Zhang. Before that, I was an undergraduate student at deparment of mathematics, Peking University, with advisor Ruochuan Liu

I am interested in arithmetic geometry and number theory. More specificly, I study integral solutions of systems of polynomial equations with integer coefficients, or equivalently, I study K-groups and motives over number fields. In my leisure time, I enjoy writing notes, snowboarding and taking road trips.

Email: (first name) _ (last name) at mit dot edu

Papers and preprints

Fargues-Scholze parameters and torsion vanishing for special orthogonal and unitary groups.
Endoscopic character relations for even special orthogonal groups, draft available upon request.
Beilinson-Bloch-Kato conjecture for polarized motives, to appear soon.
Higher Kolyvagin's theorems in the context of the arithmetic Gross-Prasad conjecture, in progress.

Expositary notes

Skyscraper project . The purpose of this project is to lay foundation for what I care about (mostly arithmetic theory of automorphic forms for now), as well as to simplify proofs and to sharpen theorems. This project is still in a primary stage. All notes I have written is contained in here. Currently it contains about 3300 pages, so it might take a while to open.
Hecke L-function for imaginary quadratic fields . A note prepared for reading course on analytic number theory with high school students.
Ternary Goldbach's problem, and average of multiplicative functions.. A note prepared for reading course on analytic number theory with high school students.

Seminars

Expository talks given

Feb 2024, On the generic part of the cohomology of non-compact unitary Shimura varieties
May 2024, Asymptotic density of rational points.
Apr 2024, Intersection matrix of basic locus via geometric Satake: examples.
Feb 2024, \lambda-adic Galois representations associated to Hilbert modular forms.
Jan 2024, \ell-adic Galois representations associated to automorphic forms.
Dec 2023, Proof of the local Langlands conjecture for GL(n) over p-adic number fields.
Oct 2023, Tate conjecture for rational K3 surfaces.
Mar 2023, Complex Abelian varieties.
Jan 2023, Kato's Euler system.
Dec 2022, Beilinson's conjecture on special values of L-functions.
Nov 2022, Conjectures about Galois representations.
Oct 2022, De Rham representations.
Oct 2022, Hodge-Tate representations.
Sep 2022, Brauer groups.
Jan 2022, Hecke converse theorems.
Oct 2021, Adic spaces.
Oct 2021, Period spaces for p-divisible groups.

Teaching

In Fall 2025 I was TA for 18.715: Introduction to Representation Theory.
In Fall 2024 I mentored three high school students on reading "Analytic number theory" by H. Iwaniec and E. Kowalski.
In Fall 2024 I was TA for 18.003: Differential Equations.
In Spring 2024 I mentored three high school students on reading "Analytic number theory" by H. Iwaniec and E. Kowalski.
In Spring 2024 I was TA for 18.786: Number Theory 2.
In Spring 2024 I was TA for 18.703: Modern Algebra.
In January 2024 I mentored one undergraduate student on reading "Local Langlands correspondence for GL(n) over p-adic fields" by P. Scholze.
In Fall 2023 I was TA for 18.112: Complex analysis in one variable.
In Spring 2023 I was TA for 18.102: Introduction to functional analysis.
In Fall 2022 I was TA for 18.112: Complex analysis in one variable.
In August 2022 I mentored one undergraduate student on wring the paper "Gelfand-Kirillov dimensions of representations of p-adic groups" during SPUR program, which won a Roger's prize for best final papers in 2022 program in undergraduate research.
In August 2022 I mentored another undergraduate student on wring the paper "Density of Tamagawa numbers of elliptic curves over global fields" during SPUR program.
In January 2022 I mentored two undergraduate students on reading "A first course on modular forms" by F. Diamond and J. Shurman.

Some useful links (very incomplete)

The following are websites that contain some information hard to be found elsewhere.

Last updated: June, 2025.

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