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

Course projects

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 R2\mathbb{R}^2 has a unique smooth structure, and more generally, a classification of noncompact surfaces with finite topology.

Notes taken by others

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.