Below are series of typset notes that I am making publically available. They are in the form of PDFs or beamer slides. Descriptions are provided above the links. Any and all comments/criticisms are appreciated, and the best way to contact me is through my contact page.
Quantum Groups Booklet
This is a booklet of typeset lecture notes for a topics in algebra class on quantum groups B. Brubaker taught during the fall 2020 semester. It assumes no background with quantum groups, strong knowledge of abstract and linear algebra, and some familiarity with representation theory (in particular highest weight theory). The booklet itself can serve as a first course in quantum groups.
Notre Dame RTG Topology & Geometry: Closed Geodesics
These are typeset notes of a talk I particularly enjoyed at the Notre Dame RTG topology & Geometry conference in 2019. The talk was delivered by gradaute student Gabor Székelyhidi on closed geodesics.
UMN REU 2020 Background Theory Notes and Exercises
These are my notes for the UMN REU in 2020. They include background theory and a few series of short exercises some of which have full solutions or partial solutions.
This section houses my raw notes, scripts, and beamer slides for all the presentations and talks I have given.
- Combinatorics of the alcove walk model (slides)
- Whittaker functions and the alcove walk model (slides)
- k-Schur functions (slides)
- Quadratic reciprocity and higher reciprocity laws (slides)
- Symmetric spaces and Cartan’s classification (script) – Symmetric spaces and Cartan’s classification (slides)
- Using holonomy to understand Riemannian manifolds (slides)
- Asymptotics of moments of Dirichlet L-series and Kac-Moody Lie algebras (script)
- The root datum of special linear and projective linear groups (script)
- The functional equation for Riemann zeta over function fields (script)
- Root systems and Hecke algebras (script)
- Representation theory and group theory (script)
- Expectancy of fixed point permutations using generating functions (script)