Algebra / Number Theory / Combinatorics Seminar

An arithmetical structure on a finite, connected graph G without loops is given by an assignment of positive integers to the vertices such that, at each vertex, the integer there […]

This talk discusses a puzzle called “Spinning Switches,” based on a problem popularized by Martin Gardner in his February 1979 column of “Mathematical Games". This puzzle can be generalized to […]

The slice rank polynomial method, motivated by groundbreaking work of Croot, Lev and Pach and refined by Tao, has opened the door to the resolution of many problems in extremal […]

Given a lattice L, an extension of L is a lattice M of strictly greater rank so that L is equal to the intersection of the subspace spanned by L […]

Markov chains have become widely-used to generate random political districting plans. These random districting plans can be used to form a baseline for comparison, and any proposed districting plans that […]

"A Tale of Two Cities" is a novel told in three books/parts. Here we describe three projects related both to published work and ongoing pieces: PROJECT 1: In the world of combinatorics, parking functions are combinatorial objects arising from the situation of parking cars under a parking strategy. In this part of the talk, we […]

Given a degree d polynomial f(x) in Q, consider the subset S_f  of Q consisting of rational numbers t for which the translated polynomial f(x) - t factors completely in Q. For example, if f is linear or quadratic then S_f is always infinite, but if degree of f is at least 3, then interesting […]

The Mahler measure of a polynomial is the modulus of its leading term multiplied by the moduli of all roots outside the unit circle.  The Mahler measure of an algebraic […]

Young diagrams are all possible arrangements of n boxes into rows and columns, with the number of boxes in each subsequent row weakly decreasing. For a partition λ of n, […]

Let  L be a full-rank lattice in R^n and write L+ for the semigroup of all vectors with nonnegative coordinates in L. We call a basis X for L positive […]

Many knot invariants are defined from features of knot projections such as arcs or crossings. Gauss diagrams provide an alternative combinatorial scheme for representing knots. In this talk we will use Gauss diagrams to enhance the biquandle counting invariant for classical and virual knots using biquandle arrow weights, a new algebraic structure without a clear […]

There are two different measures of how far a given Euclidean lattice is from being orthogonal -- the orthogonality defect and the average coherence. The first of these comes from […]