Writing
Here is a collection of mathematical writing I have done over the years. Feel free to send me an email about any typos or errors, and I’ll get to fixing them at some point.
The Smooth Representation associated to an Elliptic Curve: My Master’s essay. I talk about Local Langlands Correspondence for GL(2), introducing all the categories of representations involved. Later I discuss what the smooth representation associated to an elliptic curve via the LLC looks like.
The Fundamental Class: End of term project for a course on Global Class Field Theory. I establish the existence of the fundamental class and the fundamental exact sequence of class field theory for number fields. Assumes local class field theory and the first and second inequalities.
Cech Cohomology: End of term project for a course on Algebraic Topology. I define Cech cohomology and use it to establish the de Rham isomorphism.
The Riemann-Roch Theorem: End of term project for a course on Compact Riemann Surfaces. I give an exposition of George Kempf’s proof of the Riemann Roch theorem.
Class Number Formula and Prime Ideal Races: Slides from presentations for a topics course in analytic number theory. I talk about the analytic class number formula and generalizations of Chebyshev’s bias to prime ideals of rings of integers.