Dr. Gene Fiorini, Truman Koehler Professor of Mathematics at Muhlenberg College, will give two talks in the Mathematics and Statistics department April 7-8.
On Thursday, April 7, Dr. Fiorini will give a faculty seminar at 4:00pm (in GEM 231)
Title: Symmetric Class-0 Subgraphs and Forbidden Subgraphs
Abstract: Competition graphs and graph pebbling are two examples of graph theoretical-type games played on a graph under well-defined conditions. In the case of graph pebbling, the pebbling number pi(G) of a graph G is the minimum number of pebbles necessary to guarantee that, regardless of distribution of of pebbles and regardless of the target vertex, there exists a sequence of pebbling moves that results in placing a pebble on the target vertex. A class-0 graph is one in which the pebbling number is the order of the graph, pi(G)=|V(G)|. This talk will consider under what conditions the edge set of a graph G can be partitioned into k class-0 subgraphs, k a positive integer. Furthermore, suppose D is a simple digraph with vertex set V(D) and edge set E(D). The competition graph G(V(G),E(G)) of D is defined as a graph with vertex set V(G)=V(D) and edge vw in E(G) if and only if for some vertex u in V, there exist directed edges (u,v) and (u,w) in E(D). This talk will present some recent results on foodwebs and forbidden subgraphs of a family of competition graphs.
On Friday, April 8, Dr. Fiorini will speak in the Mathematics and Statistics Colloquium in GEM 120 at 3:30pm.
Title: CrIME: Criminal Investigation through Mathematical Examination
Abstract: Broadly speaking, forensic science analyzes trace evidence left at the scene of a crime which may be used to either implicate or exonerate a suspect, or just to gain further insight into the incident. Using several cases as a backdrop, this talk examines some of the common applications of mathematics and statistics to forensic science. Topics covered may include fingerprint analysis (graph theory, probability), blood spatter analysis (trigonometry, geometry), determining time of death (algebra, calculus), DNA identification (probability), evidence sampling (e.g. fibers, glass fragments – statistics), forensic anthropology (algebra, linear regression), and forensic entomology (statistics).