Algebra / Number Theory / Combinatorics Seminar

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 stability conditions.  In this talk, I will explain what constitutes a notion of stability in algebraic geometry, and what the challenges are in studying them.

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 been studied extensively in combinatorics, number theory, algebra, theoretical computer science and probability theory. In this talk, we will consider a reformulation of this problem […]

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 be in Euclid(0) if there exists a bijection f: V(G) --> {1,…,p} such that for each induced C3 subgraph with vertices {v1,v2,v3} with f(v1)<f(v2)<f(v3) we […]

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 […]