### DIMACS - Graduate Student Combinatorics Seminar

Title: The Genus of Graphs and Groups: An Alliterative Survey

Speaker: **Kellen Myers**, Rutgers University

Date: Wednesday, March 24, 2010 12:10pm

Location: Graduate Student Lounge, 7th Floor, Hill Center, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:
Kuratowski's theorem, a result presented in most introductory courses and texts on graph theory, characterizes precisely which graphs are planar (i.e. embeddable in the plane with no edges crossing).
Extending this characterization to other surfaces, we can define the genus of a graph to be minimal genus for a surface into which the graph embeds. We can extend this definition to a group by examining the Cayley graph of th group (with respect to some set of generators), and taking the minimum over all generating sets. This talk will attempt to introduce these concepts in a broad, survey format, with examples, illustrations, and explanations for each definition, theorem, and observation. Major results will be presented to extend and motivate the elementary concepts in the talk, as well as to give some interesting level of results, but the focus of the talk will be to introduce the material at an elementary level.

Lunch will be provided.