MATC Mathematics Club
Lecture #34
Madison Area Technical College
Madison, Wisconsin

Abstract: Graphs are used to model many real life situations, and in such circumstances graph theory serves as a foundational structure to help explain the world in which we live. One very interesting application of graph theory is in the theory of the location of facilities in networks. The theory of location of facilities in networks combines tools from graph theory, basic analysis, optimization, and complexity theory. The major focus of the theory of location of facilities on networks is to determine where to locate facilities of some sort in a network of sites that include both potential facility sites and facility user sites. Facilities might be emergency installations, supply depots, switching stations, pumping stations, power facilities, transfer stations, communication devices, obnoxious facilities, or the like. Location(s) are required that "best" serve the users, where "best" is measured by criteria given in each particular example, some of which are required to be optimized over the network. Optimality depends on criteria usually involving some ideas of distance and costs, and varies according to the application.

Biography:  Ben Collins earned a Bachelor's degree from Central College (IA), a Master's degree from the University of Michigan, and a Ph.D. from the University of Wisconsin-Madison. He has taught at Saint John's University (MN), Midland Lutheran College (NE), and is currently on the faculty of the University of Wisconsin-Platteville. His mathematical interests include graph theory, abstract algebra, and history of mathematics, and his non-Mathematical interests are Tessa (9), Ashton (6) and Quinn (2).

Professor Collins before his talk.	The audience included a large group from the Machine Tool Mathematics 2 class.
Flynn Dustrud introduces Professor Collins.	Professor Collins talks about his first slide.
	Kevin Mirus had no idea centrality in graphs could be so interesting.
Flynn Dustrud chuckles at Kevin's ignorance.
Click on any of the above pictures for the original sized image file.

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