Hao Peng

About

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 work in arithmetic geometry and number theory. My interests include integral and rational points on polynomial systems (Diophantine geometry), cohomology and motives over number fields, and the arithmetic applications of the relative Langlands program (e.g., periods, theta correspondences, and duality phenomena).

I am currently on the postdoc job market (Fall 2025). Please reach out!

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

Preprints

Fargues-Scholze parameters and torsion vanishing for special orthogonal and unitary groups. arXiv:2503.04623.
The endoscopic character identity for even special orthogonal groups. arXiv:2506.17907.
On the Beilinson-Bloch-Kato conjecture for polarized motives. arXiv:2509.18615.
Higher Kolyvagin theorems in the arithmetic Gross-Prasad setting, Ph.D. Thesis to appear.

Expositary notes

Skyscraper project . This evolving project collects my expository notes. Currently it contains about 3300 pages; 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.

Talks

Nov 2025, RTG Seminar, UC Berkeley. ''On the Beilinson-Bloch-Kato conjecture for polarized motives.''
Oct 2025, Number Theory/Representation Theory Seminar, University of Wisconsin-Madison. ''On the Beilinson-Bloch-Kato conjecture for polarized motives.''
Sep 2025, Number Theory/Representation Theory Seminar, Boston College. ''On the Beilinson-Bloch-Kato conjecture for polarized motives.''
Aug 2025, Minicourse, BICMR, Peking University. ''Arthur, Fargues-Scholze and Beilinson-Bloch-Kato.''
Jul 2025, HO#T DAY WORKSHOP (Highly Original # Theory), IASM, Zhejiang University. ''On the Beilinson-Bloch-Kato conjecture for polarized motives.''
Apr 2025, Number Theory Seminar, Boston university. ''Fargues-Scholze vs. classical parameters, and applications.''
Mar 2025, Number Theory Seminar, Stanford University. ''Fargues-Scholze vs. classical parameters, and applications.''
Mar 2025, Lie Groups seminar, MIT. ''Fargues-Scholze vs. classical parameters, and applications.''

Expositary talks

May 2025, ''Independence of \ell for Frobenius conjugacy classes attached to abelian varieties.''
Feb 2025, ''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.''

Seminars

Teaching

In Fall 2025, I was TA for 18.112: Complex analysis in one variable.
In Spring 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)

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

Last updated: Sep, 2025.

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