Expository writings

Seminar talks

Here are some notes and/or slides for various seminar talks I've given over the years.  These are not very polished, and some of them contain mathematical errors that I haven't gotten around to fixing.  Use at your own risk!

2022

• Saturated de Rham-Witt complexes with coefficients

2021

• Components of Hilbert schemes of points

2020

• Conjugate spectral sequence (also slides with and without pauses)

2019

• Gauge cohomology
• Multiplicative properties of de Rham-Witt
• Hodge-Witt cohomology
• Pathologies in p-adic and characteristic p cohomology

2018

• Crystalline comparison for AOmega via WOmega
• Étale base change of the saturated de Rham-Witt complex
• Completions of Dieudonné complexes and algebras
• Galois deformation theory

2017

• Crystalline conjecture via K-theory
• Torsion comparisons in cohomology
• A_inf-cohomology

2016

• Rational points on twisted K3 surfaces and derived equivalences
• p-adic Hodge theory
• Perfectoid spaces
• Modular curves as algebraic curves
• Shimura varieties
• Néron-Ogg-Shafarevich criterion
• Grassmannians and their Chow rings

2015

• Main Conjecture of Iwasawa theory
• Kolyvagin's theorem
• Complex multiplication
• Langlands-Tunnell theorem
• Examples of moduli spaces of sheaves on K3 surfaces
• Torelli theorem

2014

• Algebraic cycles and the Weil conjectures (.docx file)

Miscellaneous talks

• Extra algebraic points in the Chabauty-Coleman set (+ version without pauses), at Berkeley's 2021 RTG research workshop
• Special values of L-functions (+ version without pauses), at Berkeley's 2018 Undergraduate Number Theory Conference
• Torsion comparisons between de Rham and crystalline cohomology, at Arizona Winter School 2017.  (See section 3 of this seminar talk for context.)  This was my part of a joint presentation with Jesse Silliman on our strengthening of Bhatt-Morrow-Scholze Remark 14.4; it was later generalized to the log setting in Česnavičius-Koshikawa Remark 7.8.

Cornell SPUR:  generating sequences of finite groups

In summer 2017, I was the graduate assistant for Keith Dennis's undergraduate research program on generating sequences of finite groups (in which I had previously been a participant in 2013).

• Introduction and outline of research questions
• Structure and generation properties of the Rubik's Cube group (short expository talk; the "structure" part is well-known but the calculation of m(G) is new)

Miscellaneous writings

• Universal delta-functors (solution to an exercise in Ravi Vakil's algebraic geometry book, written while taking his class in 2014 and cleaned up later)
• Split fibered categories (for a reading course with Martin Olsson in 2015)
• Example of the Honda-Tate theorem (inspired by conversations at Berkeley's 2018 RTG research workshop)
• Theorem on Frobenius kernels (for a directed reading project I supervised on finite groups in 2016)
• My proof that a game of chess cannot have an infinite sequence of consecutive checks by both sides.