Here are some of my notes on various topics I have thought about. Also added are some slides for non-research talks I have given.

**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.

**Slides:**

Cyclic isogenies under isogenous elliptic curves, here.

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

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

Foray into Galois representations, here.

Topology on modular curves, here.

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

Slides on Mazur’s “Rational Isogenies of Prime Degree”, here.

Why is almost an integer, here.