## Stanford Class Notes

Notes for Math 245B, Algebraic Surfaces, as taught by Ravi Vakil in Winter 2019.

Notes for Math 245A, Algebraic Curves, as taught by Eric Larson in Fall 2019.

Notes, cowritten with Brian Conrad for Math 210C, Compact Lie Groups, as taught by Brian Conrad in Spring 2018.

Notes for Math 249A, Analytic Number Theory, as taught by Kannan Soundararajan in Fall 2017.

Notes, cowritten with Brian Conrad for Math 154, Undergraduate Algebraic Number Theory, as taught by Brian Conrad in Spring 2017.

Notes for Math 245C, Syzygies, as taught by Michael Kemeny in Spring 2017.

Notes, cowritten with Brian Conrad and Tony Feng for Math 249B, Alterations, as taught by Brian Conrad in Winter 2017.

Notes for Math 263A, Algebraic Combinatorics and Symmetric Function Theory, as taught by Persi Diaconis in Fall 2016.

## Harvard Class Notes

Notes for Math 137, Undergraduate Algebraic Geometry, as taught by Joseph Harris in Spring 2016.

Notes for Math 231br, Topological K-theory, as taught by Peter Kronheimer in Spring 2016.

Notes for Math 282, The Geometry of Algebraic Curves, as taught by Joseph Harris in Fall 2015.

Notes for Math 230a, Differential Geometry, as taught by Hiro Tanaka in Fall 2015.

Notes for Math 55b, Honors Real and Complex Analysis, as taught by Dennis Gaitsgory in Spring 2015.

Notes from the last three weeks of Math 223b, Algebraic Number Theory, proving Chebotarev's theorem, as taught by Igor Rapinchuk in Spring 2015.

Notes for Computer Science 181, Machine Learning, as taught by Ryan Adams in Spring 2014.

## Expository Writings

Exercises about moduli spaces, with a particular focus on the moduli space of curves, the moduli space of principally polarized abelian varieties, and the torelli map relating them. This was written for the 2024 Arizona Winter School on abelian varieties.

Notes on using log geometry to prove the predicted average size of l-torsion in class groups exists over fixed function fields.

Notes on reducing questions in arithmetic statistics to homological stability questions, using the Grothendieck-Lefschetz trace formula. These were used for a talk in the "No Boundaries" seminar at University of Chicago in Winter 2023.

Notes on applying relative Abhyankar's lemma to transfer monodromy between characteristics, with applications to arithmetic statistics. These were used for a talk in the arithmetic statistics seminar at Harvard Fall 2022.

Notes on applying Bhargava's methods to count number fields of degrees 2 and 3. These were written for a learning seminar on Bhargavology, run online during the coronavirus pandemic of 2020.

Notes for a talk introducing Tamagawa numbers over function fields, in preparation for Lurie's course at the 2019 Arizona Winter School.

Notes
on the classification of irreducible admissible representations of GL_{2}(ℝ) and GL_{2}(ℂ),
written for the 2017-2018 learning seminar.

A detailed account of the foundational smooth base change theorem in étale cohomology, written for the 2016-2017 learning seminar.

An expository account of the Torelli and infinitesimal Torelli theorems for curves.

An expository paper on algebraic K-theory, particularly the Grothendieck group of a scheme.

An expository paper on modular forms, proving the classification of Level 1 forms and the Four Squares theorem.

Some notes on the equivalence of three definitions of the dimension of a Noetherian local ring.

## Mathcamp Notes

#### 2023

Notes on finite fields.

#### 2022

Notes on constructing algebraic solutions to Painlevé VI through pullback.

#### 2019

Notes on counting points over finite fields.

#### 2018

Exercises on solving the cubic and quartic equations.

Exercises on the outer automorphism of S_{6}.

Notes on representations of finite groups.

Exercises on computing Galois groups of extensions of number fields using Frobenius, cotaught with Vivian Kuperberg.