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.

Continue reading## What Is a Delta Complex?

It’s time to get our hands dirty with some topology! Instead of studying spaces directly, we’re going to study a way of building topological spaces. In particular, we’re going to view a space as a collection of analogous subspaces appropriately glued together satisfying a few restrictions.

Continue reading## The Arithmetic of Polynomial Rings over Finite Fields

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## Presentation: Expectancy of Fixed Point Permutations Using Generating Functions

Here’s a script for a presentation I gave in 2018 at UMN’s Undergraduate Mathematics Research Seminar (UMRS). I spoke about using generating functions to compute the expectancy of fixed points in permutations.

Continue reading## An Introduction to Topological Groups

We’re going to talk about an interesting merger of abstract algebra and topology, namely topological groups.

Continue reading## Directed Reading Programs

Today I have something wonderful to talk about for budding mathematicians: directed readings.

Continue reading## Presentation: Representation Theory and Group Theory

The material below is a presentation I gave at the start of February in 2019 about the abelianness of groups of order using representations.

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