This page contains some of my expository notes, for which I claim no originality. Please let me know if you find any mistakes!

• Serre's Géométrie Algébrique et Géométrie Analytique (2023).

Reading report on Serre's famous GAGA. This is the final project for a course on complex geometry, lectured by Junliang Shen.

• Characteristic classes of vector bundles (2021).

A treatment of various characteristic classes of vector bundles and their properties, including Euler classes, Chern classes, and Pontryagin classes. Final project for a course on differentiable manifolds lectured by Yair Minsky.

• Hyperbolic geometry and the Bruhat--Tits trees (2020).

An exploration of the analogy between the complex upper half plane and the Bruhat--Tits tree of a given prime. Final project for a course on algebraic number theory lectured by Alexander Goncharov.

• Introduction to Shimura varieties (2020).

An introduction to the modern theory of Shimura varieties, following the first six chapters of Milne's notes. This is my undergraduate thesis, supervised by Zhiyuan Li and written in Chinese.

• On Burgess' estimate, quadratic residues and non-residues (2019).

Applied D. A. Burgess’ estimate on character sums to some problems in quadratic residues and non-residues. Final project for a course on analytic number theory lectured by John Friedlander.