This is a presentation I gave for my Algebraic Number Theory class during the Spring 2019 semester. In it I prove the functional equation for the Riemann zeta function for global function fields of transcendence degree one. The written version here quite closely resembles the talk I gave, so the edits are slim to none.… Continue reading Presentation: ANT Spring 2019
Yet another presentation! Below is a written version of a presentation I gave for the DRP program during the spring of 2019. The presentation is on root systems and Hecke algebras, the main idea being to introduce the flavor of these topics. The version here is significantly extended than what I spoke about so that… Continue reading Presentation: DRP Spring 2019
Welcome to a new collection of posts that will consist of semi-constantly updated notes for several graduate level mathematics texts. To give some background, I tend to notate my books fairly heavily and in a manner that makes it easier for myself to read through them if I ever need to review something. I've decided… Continue reading Graduate Text Notes
It's time to get our hands dirty with some topology! Instead of studying spaces directly, we're going to study a way of studying a topological space (sort of meta, but that's the fun of it). In particular, we're going to view a space as a collection of analogous subspaces appropriately glued together satisfying a few restrictions.… Continue reading What Is a Delta Complex?
Today we're going to talk about something quite exciting and unexpected: the arithmetic of polynomial rings over finite fields and its similarity to the arithmetic of the integers. We'll first run though some preliminary observations about the arithmetic of the polynomial rings which will suggest that it behaves similar to the arithmetic of the integers.… Continue reading The Arithmetic of Polynomial Rings over Finite Fields
Here's another written version of a presentation I gave in 2018 at UMN's USMR (undergraduate mathematics research seminar). I spoke about using generating functions to compute the expectancy of fixed points in permutations. Some of the proofs in this talk are technical, so I've decided to cut them and only present the critical ones. After… Continue reading Presentation: UMRS Spring 2018
Hey there, and welcome back! Today we're going to talk about an interesting merger of abstract algebra and topology, namely topological groups. Last week a colleague asked me if there were any mathematical topics which were used in class but that I was never previously taught. While I do self study a lot, I had… Continue reading An Introduction to Topological Groups