2007 Section Meeting

Invited talks

Margaret Robinson, Mount Holyoke College

Bright Lights on the Horizon

Abstract: What do a square-wheeled bicycle, a 17th-century French painting, and the Indiana legislature all have in common? They appear among the many bright stars on the mathematical horizon, or perhaps, more correctly in the Math[ematical] Horizons. Math Horizons, the undergraduate magazine started by the MAA in 1994, publishes articles to introduce students to the world of mathematics outside the classroom. Some of mathematics’ best expositors have written for MH over the years; here are some of the highlights from the first ten years of Horizons.

Fred Roberts, Rutgers University and DIMACS

Consensus List Colorings of Graphs and Physical Mapping of DNA

Abstract: In graph coloring, one assigns a color to each vertex of a graph so that neighboring vertices get different colors. We shall talk about a consensus problem relating to graph coloring and discuss the applicability of the ideas to the DNA physical mapping problem. In many applications of graph coloring, one gathers data about the acceptable colors at each vertex. A list coloring is a graph coloring so that the color assigned to each vertex belongs to the list of acceptable colors associated with that vertex. We consider the situation where a list coloring cannot be found. If the data contained in the lists associated with each vertex are made available to individuals associated with the vertices, it is possible that the individuals can modify their lists through trades or exchanges until the group of individuals reaches a set of lists for which a list coloring exists. We describe several models under which such a consensus set of lists might be attained. In the physical mapping application, the lists consist of the sets of possible copies of a target DNA molecule from which a given clone was obtained.

James Sellers, Penn State University

Research in Integer Partitions: Alive and Well

Abstract: In this talk, I will gently introduce you to the basics of the subject and discuss some of the people who have inspired research in the field over the last several years. I will also prove some well-known partition-theoretic results, including Euler's famous result that the number of partitions of an integer n into odd parts equals the number of partitions of n into distinct parts. This result is approximately 250 years old, but is by no means "dead". I will demonstrate some results related to this one which have arisen quite recently (within the last year). My hope is that all will find this talk refreshing and that some will be spurred on to future studies in partitions.