Talks & Notes

Expository write-ups and slides from various seminars and conferences.

Research Talks

Research

Generalized Fontaine-Laffaille theory

Sep 2026

Talk at the Joint PU/IAS Arithmetic Geometry Seminar. Joint work with Shubhodip Mondal.

Research

Isogenies, $p$-Hecke correspondences and Rapoport-Zink spaces

Jan 2026

Talk at AIM Special Session on Arithmetic Geometry of Shimura varieties at the JMM 2026

Research

Overview of the construction of derived cycles

Feb 2025

Talk at a workshop in Darmstadt on special cycles on Shimura varieties

Expository talks

Expository

BC Undergraduate Colloquium on Fermat's Last Theorem

Nov 2025

Talk targeted at undergrads about the history of Fermat's Last Theorem and its resolution by Andrew Wiles

Parsing AI proofs

Notes

Milne's rationality conjecture

Oct 2026

The first proof in the OpenAI dump on Oct 6, 2026 was a proof of a rationality conjecture of Milne. Its organization and exposition were characteristically incomprehensible, but the underlying idea turns out to be quite simple and quite clever, as I discovered after waterboarding Astra 6 into revealing it to me.

Miscellanea

Letters

Grothendieck's letter to Illusie

Dec 1969

Letter from Grothendieck to Illusie where he sketches a proof of the smoothness of the stack truncated Barsotti-Tate groups

Old notes from graduate school

Notes

Log $p$-divisible groups after Kato

Sep 2009

Exposition of work of Kato on log $p$-divisible groups. Kato's paper is now available on the arXiv .

Notes

Commutative algebra

Sep 2007
Notes

Algebraic geometry

Sep 2007
Notes

Homological algebra

Sep 2007
Notes

Noetherian spaces

Sep 2007
Notes

Notes on sheaves

Sep 2007
Notes

Ringed spaces

Sep 2007
Notes

$D$-modules

Jan 2008

Notes from a course on $D$-modules taught by Victor Ginzburg .