An “Adinkra” is a graphical tool to describe a branch of particle physics known as supersymmetry. Understanding the mathematics of Adinkras shines a light on the underlying physics, as well as helps to explore new areas of mathematics. After describing the basic structure of Adinkras, I will discuss some of these interesting interactions between mathematics […]
The classical, one-boundary, and two-boundary Temperley-Lieb algebras arise in mathematical physics related to solving certain rectangular lattice models.They also have beautiful presentations as "diagram algebras", meaning that they have basis […]
In this talk, I will give an overview of the theory of matroids. These are mathematical objects which capture the combinatorial essence of linear independence. Besides providing some basic definitions […]
A classic and fundamental result in number theory is due to Mordell who proved that the set of points on an elliptic curve defined over a number field forms a […]
Counting points on algebraic curves over finite fields has numerous applications in communications and cryptology, and has led to some of the most beautiful results in 20th century arithmetic geometry. A natural generalization […]
If $F$ is a finite field and $d$ is a positive integer relatively prime to $|F^\times|$, then the power map $x \mapsto x^d$ is a permutation of $F$, and so is called […]
Mathematicians like to count things. Often in very complicated and fancy ways. In this talk I will explain how we can use quantum Airy structures -- an abstract formalism recently […]
We review some recent developments in the study of biquandle brackets and other quantum enhancements.
Domination in graphs has been an important and active topic in graph theory for over 40 years. It has immediate applications in visibility and controllability. In this talk we will […]
Probability is a now-classic tool in combinatorics, especially graph theory. Some applications of probabilistic techniques are: (1) describing the typical/expected properties of a class of objects, (2) uncovering phase transitions […]
Probability is a now-classic tool in combinatorics, especially graph theory. Some applications of probabilistic techniques are: (1) describing the typical/expected properties of a class of objects, (2) uncovering phase transitions […]
In this talk, I will describe an approach to finding upper bounds for the number of arithmetic operations necessary for doing harmonic analysis on permutation modules of finite groups. The approach takes advantage of the intrinsic orbital structure of permutation modules, and it uses the multiplicities of irreducible submodules within individual orbital spaces to express […]
