# Interests

I study interactions between algebraic geometry, number theory, and representation theory. I am also interested in syntax. Here is an incomplete and unordered set of words and phrases I find compelling:

$$p$$-adic, nonarchimedean, adic space, perfectoid, pro-étale, overconvergent, (bounded) Robba ring, D-module, perverse sheaf, rigid cohomology, de Rham(-Witt), crystalline, $$\mathbb{A}_{\mathrm{inf}}$$, prismatic, condensed, pyknotic, locally analytic representation, Langlands correspondence, Riemann-Hilbert correspondence, Beilinson-Bernstein localization, Fargues-Fontaine curve, cotangent complex, category, derived, homological, topos, derivator, categorial grammar, minimalist program, …

# Talks

Here are slides/notes for some of my past talks. If you find any errors in these, please let me know!

• From category $$\mathcal{O}^\infty$$ to locally analytic representations. Two versions:
• Rennes. May 2021 at the Séminare géométrie arithmétique at the Institut de recherches mathématique de Rennes. This talk includes more background material compared to the Padova version below.
• Padova. 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. This talk assumes some background material that had been discussed in preceding seminar talks.
• 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.

# Miscellaneous

Here are some miscellaneous writings. If you find any errors in these, please let me know!

• PhD Thesis. Contains more expository content than the published version.
• Off on a Tangent. Some notes about several incarnations of the derivative, for a real analysis course I taught.
• 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.
• Undergraduate Honors Thesis. Written during 2010–2011.