Algebra / Number Theory / Combinatorics Seminar

Given a homogeneous multilinear polynomial F(x) in n variables with integer coefficients, we obtain some sufficient conditions for it to represent all the integers. Further, we derive effective results, establishing […]

In this talk we will survey recent developments in the use of ternary algebraic structures known as Niebrzydowski Tribrackets in defining invariants of knots, with some perhaps surprising applications.

In this talk we introduce a new modification of the Jacobi-Perron algorithm in the three dimensional case. This algorithm is periodic for the case of totally-real conjugate cubic vectors. To […]

When first learning how to write mathematical proofs, it is often easier for students to work with statements using the universal quantifier. Results that single out special cases might initially […]

The Kauffman bracket skein algebra was originally defined as a generalization of the Jones polynomial for knots and links on a surface and is one of the few quantum invariants […]

A Belyi map $\beta: \mathbb{P}^1(\mathbb{C}) \to \mathbb{P}^1(\mathbb{C})$ is a rational function with at most three critical values; we may assume these values are $\{ 0, \, 1, \, \infty \}$. […]

The complete homogeneous symmetric (CHS) polynomials can be used to define a  family of norms on Hermitian matrices. These 'CHS norms' are peculiar in the sense that they depend only on the […]

It is widely believed that Weierstrass ignored Eisenstein's theory of elliptic functions and developed an alternative treatment, which is now standard, because of a convergence issue. In particular, the Eisenstein […]

We consider the problem of comparing the number of discrete points that belong to a set with the measure (or volume) of the set, under circumstances where we expect these […]