Abstracts for MathFest08
From CanisiusmathWiki
TITLE: Graphs, Coverings, and Characteristic Polynomials
PRESENTERS: Gabrielle Paoletti and Rachel Hunter
ABSTRACT: By the spectrum of a directed graph we mean the eigenvalues of its adjacency matrix, determined by its characteristic polynomial. When a large graph is a covering of a small graph, the second characteristic polynomial is a factor of the first. There are many interesting examples. (This talk will present results from this summer's investigations at the Canisius College REU, Geometry and Physics on Graphs.)
TITLE: Crystals and quasicrystals via algebraic graph theory and groupoids
PRESENTERS: emily bargar and Vivian Healey
ABSTRACT: We study crystal and quasicrystal infinite graphs via two general tools. One tool is the notion of groupoid, including toplogical structure. The other tool is the spectra of families of finite graphs formed by truncating or wrapping the infinite graph. (This talk will present results from this summer's investigations at the Canisius College REU, Geometry and Physics on Graphs.)
TITLE: Directed graphs and groupoids
PRESENTERS: Brian Leary and Colin Klaus
ABSTRACT: Given a directed graph, it is known that one can associate to it a certain (topological) groupoid. As a next step, one investigates the relationships between various groupoid operations (product, sum, subgroupoid, induced groupoid, etc.) and manipulations at the graph level. While some results are already known, there are still cases where the knowledge is limited (like the notion of the zig-zag product of graphs). The talk will report on any progress made in enriching the relationship, using several examples. (This talk will present results from this summer's investigations at the Canisius College REU, Geometry and Physics on Graphs.)
TITLE: Random Walks and Geometry of Directed Graphs
PRESENTERS: Ariel Binder and Joshua O'Rourke
ABSTRACT: Any locally finite directed graph determines a random walk, determined by a Markov chain. We apply techniques from algebraic graph theory to the study of interesting graphs coming from group theory and geometry. (This talk will present results from this summer's investigations at the Canisius College REU, Geometry and Physics on Graphs.)
