Here are some notes I have written as a postdoc and as a graduate student, as well as some slides for non-research talks I have given. 

Course Notes:

Here are notes from a graduate topics class that I taught on the arithmetic of elliptic curves at Ohio State in Spring 2025 (191 pages). They are supplemental to Silverman’s book of the same name (second edition), with added comments and details, as well as a “chapter zero” on elliptic curves from a planar perspective that should be accessible to a broad range of students.

Older Notes:

Supplemental notes to Serre’s “Propriétés galoisiennes des points d’ordre fini des courbes elliptiques” on the open image theorem for non-CM elliptic curves, here.

Supplemental notes to Mazur’s “Rational isogenies of prime degree”, here.

Supplement to Section 12 from Neukirch’s “Algebraic Number Theory” on class numbers of orders in number fields, here.

Older Slides:

Constructible numbers, division points and class field theory, here.

Foray into Galois representations, here.

Topology on modular curves, here.

Why is almost an integer, here.

Slides on Mazur’s “Rational isogenies of prime degree”, here.

Serre’s adelic open image theorem for non-CM elliptic curves (handwritten), here.

Entanglements of Galois representations of CM elliptic curves (handwritten), here.