Algebra / Number Theory / Combinatorics Seminar

Suppose you are given a data set that can be viewed as a nonnegative integer-valued function defined on a finite set. A natural question to ask is whether the data […]

An elliptic curve $ E: y^2 + a_1 \, x \, y + a_3 \, y = x^3 + a_2 \, x^2 + a_1 \, x + a_6 $ is […]

The existence of a set $A\subset \N_0$ of positive upper Banach density such that $A-A:=\{m-n:m, n\in A, m>n\}$ does not contain a set of the form $S-S$ with $S$ a piecewise syndetic is in essence the content of a popular result due to K\v r\'{i}\v z in 1987. Since then at least four different proofs […]

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 is a divisor of the sum of the integers at adjacent vertices, counted with multiplicity if the graph is not simple. Alternatively,  an arithmetical structure […]

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 a two-player game on a finite wreath products. This talk will provide a classification of several families of these generalized puzzles, including a full classification […]

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 combinatorics. We survey these results and discuss contributions in several of the speaker's recent papers.

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 […]

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 […]

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, […]