Davidson Lecture Hall, CMC

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 […]

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 […]

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 […]

"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 […]

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 […]

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 with M. In this talk, we will discus constructions of such lattice extensions with particular geometric invariants of M, such as the determinant, covering radius […]

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.

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 […]

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 […]

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 […]