Augusta Ada Byron King Lovelace (1815-1852) is today celebrated as the first computer programmer in history. This might be confusing to some because in 1852 there were no machines that […]
One of the main drivers of current research in geometry is the classification of Calabi-Yau threefolds. Towards this effort, a particular approach in algebraic geometry is via the study of […]
The classical Frobenius problem asks for the largest integer not representable as a non-negative integer linear combination of a relatively prime integer n-tuple. This problem and its various generalizations have […]
In Euclidean geometry, the sum of two sides of any triangle is greater than the third side. We introduce this idea to labeling of graphs. A (p,q)-graph G=(V,E) is said to […]
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 […]
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.
