Professor Archdeacon will study width parameters of embedded graphs, embedding properties of covering graphs and the lifting properties of embedded graphs. The proposed research studies new techniques for coverings and wrapped coverings and applies these techniques to topological graph theory. Graph Theory goes back perhaps two hundred years, but only in the last half-century has the field become an active, fertile, and flourishing branch of mathematics. A graph is a network of lines ("edges") joining points ("vertices"), thus the language of graphs becomes a natural way of describing interrelationships among separated objects. Graph Theory figures most prominently as an essential tool in Communications Theory and Computer Science.
