Hanson Hao

I am a third year graduate student at Berkeley, interested in arithmetic geometry and number theory. I am fortunate to be advised by Yunqing Tang. Previously, I earned a B.S. in Mathematics and a M.S. in Statistics from Stanford University.

Currently, I am learning/thinking about Arakelov geometry and Diophantine problems involving higher-genus curves. I also enjoy ideas arising from arithmetic dynamics.

Email: first initial last name AT berkeley DOT edu

Office: Evans 787

I am not teaching in Spring 2026.

Papers/Notes/Articles

Notes and Expository Writings

Two Applications of Bigness
Rank one abelian Stark conjecture
Adelic Line Bundles and Bogomolov's Conjecture (very rough notes)
1-Dimensional Arakelov Geometry
Notes on Algebraicity and Holonomy Criteria
My syllabus and rough transcript from my qualifying exam

Undergrad Stuff

My senior thesis (advised by Brian Conrad).
Polarizations of equigenerated strongly stable ideals (with Yuyuan Luo and Sterling Saint Rain).
Some Algebraic Properties of ASM Varieties (with Ilani Axelrod-Freed, Matthew Kendall, Patricia Klein, and Yuyuan Luo). Glasgow Mathematical Journal, to appear.
Investigations on automorphism groups of quantum stabilizer codes. arXiv:2109.12735.

Seminars Organized

Arakelov Geometry Learning Seminar, Spring 2025
Class Field Theory Reading Group, Fall 2023-Spring 2024

Teaching/Mentoring

I was a mentor for the Berkeley "Numbers, Symmetry, and Geometry" RTG REU in Summer 2025. I have also been a mentor for the Berkeley DRP for the past two years.

Math 55: Summer 2024

Course Webpage

Math 54: Spring 2024, Spring 2025

Midterm 1 Study Guide (Linear Systems, Vector Spaces, Linear Maps, Determinants)
Midterm 2 Study Guide (Change-of-basis, Rank-Nullity, Eigenvalues, Inner Products, Spectral Theorem)
Brian Sun's notes on Differential Equations

Math 1B (now Math 52): Fall 2023

Midterm 1 Study Guide (Integration Techniques)
Midterm 2 Study Guide (Sequences and Series)
Midterm 3 Study Guide (ODEs)