Speaker: T. Kyle Petersen (DePaul University)

Title: Eulerian Numbers

Abstract: Every student of mathematics is familiar with Pascal's triangle of binomial coefficients. Though not as well known, the classical Eulerian numbers form a triangle that is almost as nice. These numbers have been given many different combinatorial interpretations, as well as algebraic and geometric interpretations. Via the algebraic and/or geometric interpretations, we can generalize the Eulerian numbers in many ways, e.g., to Coxeter groups, or to certain families of polytopes. I will survey some of the history of Eulerian numbers, including current work and open problems.