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 […]
Hassett spaces in genus 0 are moduli spaces of weighted pointed stable rational curves; they are important in the minimal model program and enumerative geometry. We compute the Chow ring of heavy/light Hassett spaces. The computation involves intersection theory on the toric variety corresponding to a graphic matroid, and rests upon the work of Cavalieri-Hampe-Markwig-Ranganathan. […]
We will discuss the sparsity of the solutions to systems of linear Diophantine equations with and without non-negativity constraints. The sparsity of a solution vector is the number of its nonzero entries, which is referred to as the 0-norm of the vector. Our main results are new improved bounds on the minimal 0-norm of solutions […]
In this talk we discuss some problems related to finding large induced subgraphs of a given graph G which satisfy some degree-constraints (for example, all degrees are odd, or all degrees are j mod k, etc). We survey some classical results, present some interesting and challenging problems, and sketch solutions to some of them. This […]
Let d >= 2 be a natural number. We determine the minimum possible size of the difference set A-A in terms of |A| for any sufficiently large finite subset A […]
