# Overview

I study algebraic geometry: more specifically, I am interested in \(p\)-adic cohomology theories and \(p\)-adic analytic geometry.

Here are some mathematical phrases that I find exciting/intriguing: \(p\)-adic, nonarchimedean, adic space, perfectoid, pro-étale, overconvergent, (bounded) Robba ring, (arithmetic) D-module, rigid cohomology, de Rham(-Witt), crystalline, cotangent complex, (higher) category, derived, homological, topos, derivator, non-noetherian, …

I completed my PhD at UC Berkeley in 2018. My advisor was David Nadler.

# Papers

All papers at arXiv.org/a/agrawal_s_1.

- From category \(\mathcal{O}^\infty\) to locally analytic representations. With Matthias Strauch. arXiv:2011.12370. Submitted.
- Deformations of overconvergent isocrystals on the projective line. arXiv:1710.03404. doi:10.1016/j.jnt.2019.11.013.

My PhD thesis is available here. There are a few typos in this document, but they’re not terribly serious. The arXiv and published versions correct these typos, but they do omit some of the expository content that’s in my thesis.

# Talks

Here are some slides and/or notes for some of the talks I’ve given.

- From category \(\mathcal{O}^\infty\) to locally analytic representations. Notes from a talk I gave (about the paper of the same name) in April 2021 at the
*p-adic representations and arithmetic D-modules*seminar, organized by Andrés Sarrazola Alzate and Francesco Baldassari, at the Università degli Studi di Padova. - Perspective: The Mathematics of Depicting Depth. Slides for a talk I gave at Colorado College’s
*Fearless Fridays*seminar in February 2020. - A Smörgåsbord of Arithmetic Geometry. Slides for a talk I gave at Colorado College’s
*Fearless Fridays*seminar in February 2018. - Contangent complex. Some (incomplete!) notes I compiled when I was preparing for a talk I gave in David Nadler’s fall 2013
*geometric representation theory*seminar.

If you find errors in any of these, please let me know!

# Miscellaneous

Here are some miscellaneous mathematical writings.

- Off on a tangent. Some notes about derivatives.
- Exponential at infinity. A fun explicit calculation I did during summer 2017 involving an irregular rank 1 overconvergent differential module over the Robba ring.
- Fundamental group of a curve. An expository term paper from Martin Olsson’s Spring 2012 Algebraic Geometry course.

If you find errors in any of these, please let me know!