Andy Gordon

These are notes for the talk I gave on the the Brauer-Manin obstruction to rational points for the a seminar at the University of Michigan in Fall 2022. In the talk I computed the Brauer-Manin set to prove results about rational points for a few different varieties.

This is a final paper written for a course in analytic number theory. I give an overview of Deligne's use of étale cohomology to bound certain trigonometric sums.

These are notes for the talk I gave on the geometric Satake isomorphism for the a seminar at the University of Michigan in Spring 2022. There are very few proofs, but the talk provides an outline of the construction in the case of GL₂ for an unfamiliar audience.

These are notes for a talk I gave on Deligne-Lusztig theory in a seminar at the University of Michigan. The talk used the Drinfeld curve to find irreducible characteristic 0 representations of the group SL₂(k) for k a finite field, following Bonnafé's book Representations of SL₂(F_q) .

These are notes for a talk I gave on Schubert Calculus in a seminar at the University of Michigan in Spring 2019. The goal was to motivate the ideas of intersection theory by answering the question "How many lines in projective 3-space meet four general lines?"