Dr. Geir Agnarsson, 2 October, 2006
 Kissing Numbers of Spheres and Related Extremal Tangency Graphs.

Abstract:  A unit coin graph is a simple graph the vertices of which can be represented by points in the Euclidean plane in such a way that (i) the distance between every two points is at least one, and (ii) two vertices are connected if the Euclidean distance between the corresponding points is exactly one. Paul Erdos and others have asked for the maximum number for a unit coin graph on fixed number of vertices. Although this problem is completely solved, many other related problems are still open and far from solved.

In this talk we discuss some partial results in higher dimension than two and discuss the kissing number for spheres and the upper bound for the maximum number of edges a corresponding tangency graph on a fixed number of vertices can have.


Biographical sketch: Born in Norway, grew up in Italy and Iceland. Received a BS in mathematics from the University of Iceland in 1990, and a PhD in pure mathematics from the University of California at Berkeley in 1996. Has been a Postdoctoral Researcher at the Science Institute, University of Iceland, Visiting Scholar at Arizona State University and Los Alamos National Laboratory among other places. Is currently an Assistant Professor at George Mason University since 2002. -- Enjoy travelling, ethnic food, music the outdoors (skiing and hiking) and every form of physical activity.