## Exposition

### Notes for Talks Given

Jul. 2016 - The Different Flavors of the Modularity Theorem. Purdue Number Theory Seminar

Apr. 2016 - Faltings' Theorem Part I: Algebraic Geometry for Number Theorists. Purdue Secret Seminar

July 2015 - A Riemann-Roch Theorem for Number Fields and Sheaves. Purdue Riemann-Roch Seminar.

Sept. 2013 - Abelian Kummer Theory. Purdue Number Theory Seminar

April 2012 - Proper Prime Representing Functions. Purdue Number Theory Seminar

**Translations**

Isogénies Entre Coubres Elliptiques by Jacques Vélu (orginal in French)

**Misc. Math Notes**

An Overview of Modern Mathematics Through the Topics of the SAT