Talks

Here are the slides for some of the talks I have given:

• Realizability of Graphs: These slides are a modified version of the 20 minute talk I gave at the Horizon of Combinatorics conference at Lake Balaton, Hungary, in July 2006.

  Abstract: A graph is d-realizable if, for every realization of the graph in some Euclidean space, there exists a realization in d-dimensional Euclidean space with the same edge lengths. For example, any tree is 1-realizable, but a triangle is not. In this talk, we will classify all 3-realizable graphs. This talk is based on joint research with Robert Connelly.

• Realizability of Graphs: This is a version of the above talk that was aimed at undergraduates attending the Carleton Summer Math Program during the summer of 2007.


• Making Your House Safe from Zombie Attacks: I gave this talk at the AMS-MAA Joint Meetings in January 2008.

  Abstract: We investigate the important question of how many zombies are required to catch and eat a person in an enclosed structure. We model the structure with a graph, and we assume that the person can move much faster than the zombies. The minimum number of zombies required to catch an intelligent person is called the zombie number of the graph. This is a variation on the "cops and robbers" game from graph theory, which can be used to define the treewidth of a graph. In this talk, we will discuss how the zombie number of a graph relates to the treewidth, and we will investigate forbidden minors for zombie number n. This talk will assume no prior knowledge of graph theory, and should be accessible to undergraduates. This talk is based on ongoing research with Jim Belk.

• Problems related to the Kneser-Poulsen Conjecture: I gave this talk in Fall 2007 in the Algebra and Combinatorics seminar at Texas A&M.

  Abstract: Consider a collection of overlapping balls in Euclidean space. If we change the positions of the balls, then the volume of the union may change. In the 1950's, Kneser and Poulsen conjectured that if the distances between the centers do not decrease, then the volume of the union must increase or remain the same. In 2002, Bezdek and Connelly proved this conjecture for discs on the Euclidean plane. The conjecture remains open for higher dimensional Euclidean spaces, as well as for spherical and hyperbolic spaces. In this talk, we will examine the difficulties involved in extending the proof to these other settings.