I'm an undergraduate mathematics and computer science major at Carnegie Mellon University. In the fall of 2014, I'll be participating in the Math in Moscow program at the Independent University of Mathematics.
My email is adsmith [at] andrew [dot] cmu [dot] edu.
My CV can be found here.
Starting in the fall of 2014, I'm going to keep sporadic lecture notes here for my classes. I make no promises about keeping these up-to-date, but the general goal is to post them shortly after each lecture. Ideally this will force me to make sure I understand each lecture, and provide a useful reference to me or anybody else to look back at.
In the summer of 2014, I participated in the SUMaR math REU at Kansas State University. My advisor was Alex Gonzalez. My project focused on generalizing a notion of Euler characteristic for finite categories to certain infinite categories arising from the homotopy properties of compact Lie groups. We also provided a geometric reinterpretation of these objects as certain sheaves over a Grothendieck site.
Our writeup can be found here.
In the summer of 2013 I did an REU at Clemson University. There my advisor was Mohammed Tesemma. My project studied rings of invariants in the Laurent polynomials of subgroups of the general linear group. We placed a natural topological structure on their space of different initial algebras under all possible monomial orders.
A preprint of the resulting paper can be found here. Here are slides on our results.
In the spring of 2014 I taught 15-453 Formal Languages, Automata, and Computability. The course website can be found here.