## Presentation: Using Holonomy to Understand Riemannian Manifolds

This is the script for a presentation I gave for a class in Riemannian Geometry at the University of Minnesota in the Fall of 2019. In it, I dicuss the basics of holonomy, history of the theory, de Rham’s decomposition theroem, the Ambrose-Singer theorem, and Berger’s classifiction. Motivation Let us start with an example to … Continue reading Presentation: Using Holonomy to Understand Riemannian Manifolds

## Presentation: The Root Datum of Special Linear and Projective Linear Groups

This is the script for a presentation I gave for the Directed Reading Program at the University of Minnesota in the Fall of 2019. In it, I dicuss how the root datum is an extension of the root system, and how we can use it to distinguish between linear algebraic groups. Motivation In the following … Continue reading Presentation: The Root Datum of Special Linear and Projective Linear Groups

## Presentation: Asymptotics of Moments of Dirichlet L-series and Infinite Kac-Moody Lie Algebras

I’ve been incognito for the last few months due to classes and research interests. More posts are comming in the following weeks to compensate for this absence. In other new, this is a presentation I gave for the Student Number Theory Seminar at the University of Minnesota in the Fall of 2019. Abstract Understanding the … Continue reading Presentation: Asymptotics of Moments of Dirichlet L-series and Infinite Kac-Moody Lie Algebras

## Measurable Spaces & Topological Spaces, an Analogy

While I was in Indiana a few weeks ago at Notre Dame for their Geometry & Topology conference I had a very enlightening conversation with my roommate at the time (and now good friend). He had come across a small section in one of Rudin’s analysis textbooks which highlighted an analogy between measurable spaces and … Continue reading Measurable Spaces & Topological Spaces, an Analogy

## Geometry & Topology RTG

Previously this week (week of August 3rd) I was able to attend the Geometry & Topology RTG workshop at the University of Notre Dame. The workshop was a week long event consisting of two parts, I and II, the first being an introduction into geometry & topology, and the latter being lectures on more advanced … Continue reading Geometry & Topology RTG

## Presentation: The Functional Equation for Riemann Zeta Over Function Fields

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: The Functional Equation for Riemann Zeta Over Function Fields

## Presentation: Root Systems and Hecke Algebras

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: Root Systems and Hecke Algebras