For centuries finding the determinant of a matrix was considered to be something that took $\Theta(n^3)$ steps. Only in 1969 did Strassen discover that there was a faster method. In […]
In this talk, I will try to give a fun introduction to tropical geometry and Hassett spaces, and show how tropical geometry can be used to compute the Chow rings […]
A triple of natural numbers (a,b,c) is an S-set if a+b=c. I. Schur used the S-sets to show that for n >3, there exists s(n) such that for prime p […]
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 […]
