**Moduli of curves and multiple roots**, submitted

**On pairs of theta characteristics**, in preparation

# Thesis

**Enumerative geometry of double spin curves**

# Notes

**Twistor connectivity of the cohomological moduli spaces**

This is a detailed exposition of Section 4 in Buskin’s paper. The goal is to show that moduli spaces parametrizing pairs of K3s and a rational Hodge isometry between them are connected by “twistor” paths. In these notes we bypass some calculations of Buskin on the variation of complex structures on products of K3s and reduce it to a tautology.

**Deformation Theory lecture notes 3-10**

Typed up version of Michael Kemeny’s handwritten lecture notes which can be found here. I added some fluff according to personal taste.

**Finiteness of isogeny classes**

We give a detailed exposition of the proof that there are only finitely many isogeny classes of abelian varieties (of fixed dimension, and with good reduction outside of a fixed finite set). Lecture notes for my talk in IRTG College Seminar, Summer 2015, with the goal of understanding Falting’s Theorem.

**Line bundles and cohomology of complex tori**

A summary of Chapter 1 in Mumford’s book “Abelian Varieties” covering complex compact abelian varities, i.e., complex tori. This is a lecture note for my talk on IRTG College Seminar, Winter 2014/15, with title “Abelian Varieties and Derived Categories”.

**Elliptic curves and automorphic forms**

An introduction to automorphic forms from an algebraic perspective. Hence, you get to see them as sections of line bundles on modular curves. These are my lecture notes for IRTG College Seminar, Summer 2014, with the general theme of understanding Fermat’s Last Theorem.