Writings

These are notes for seminars that I hosted as an undergraduate student at Tsinghua University.

Homotopical Algebra and Homological Algebra (2019).
Notes on $\infty$ -categories. Chinese version available here.
Characteristic Classes (2019, in Chinese).
Notes on characteristic classes and the Atiyah–Singer index theorem.

Some of the projects that I did for courses contain little pieces of original results, and I post them here.

Homology of Configuration Spaces (2020).
A method to compute the homology of configuration spaces of manifolds.
Stable Irrationality of Varieties (2020).
Proves the infinitude of stable birational classes in certain families of varieties.
A Generalised Handle Theory (2018).
Generalises handle theory to noncompact manifolds. This leads to a new proof that $\mathbb{R}^2$ has a unique smooth structure, and more generally, a classification of noncompact surfaces with finite topology.

Here are notes of some of my talks that are taken by other people.

Higher Geometry (2023, notes by Tommi Muller).
I gave the first two talks, which were an introduction to the theory of algebraic stacks.