Writings

Some notes I made while learning about étale cohomology. These notes are probably incomplete. These notes are also fairly terse, as I was just trying to summarise some results that I thought were important. This is in no way comprehensive

Some notes I am making while I learn the theory of automorphic vector bundles on Shimura varieties. These notes are incomplete.

Some notes I made while studying for Harvard’s qualifying exam, held in the last week of August 2022. I did not put much effort into the chapters on algebra and the complex analysis, as I felt extremely comfortable with them. In particular, in the complex analysis chapter, I also barely put any effort into the section on conformal maps, which (as it turns out) was a bad idea. I also did not study for algebraic topology for the quals, and so there is no chapter on algebraic topology. With these caveats out of the way, I think (and have been told) that the notes are fairly good for preparing for the other five subjects on the Harvard quals.

Some notes I am making while I learn about the differential theory of schemes. In particular, I am looking at (relative) de Rham cohomology of quasi-coherent sheaves on arbitrary schemes and the theory of connections on such sheaves. In particular, I will probably focus on three things: (1) connections in positive characteristic, (2) canonical extensions of connections and bundles over divisors, and (3) (abelian and non-abelian) Hodge theory. These notes are partly motivated by the seminar on non-abelian Hodge theory running at Harvard. These notes are incomplete.

Lecture notes for a summer tutorial. See [this](https://kush1729.github.io/teaching/2023/summer-quadratic_forms/).

Notes for an introductory talk on the geometry of the smooth Artin stack $\mathrmBun(G)$.