(Enumeration Results for) Signed Graphs

Signed graphs originated in the social sciences and have found applications also in biology, physics, computer science, and economics. A signed graph stems from an ordinary graph whose edges have been declared either as positive or negative. The signed analogue of a directed graph/network is a bidirected graph, for which each edge has an independent orientation at each of its end points. This talk will give an introduction to the mathematics of signed and bidirected graphs, with a view towards enumeration. For example, we will illustrate how chromatic and flow polynomials generalize to the setting of signed graphs.

Speaker Bio: Matthias Beck studied at the University of Würzburg, SUNY Oneonta, and Temple University. After postdoctoral positions at SUNY Binghamton, the Mathematical Sciences Research Institute, and the Max-Planck-Institute in Bonn, he arrived at San Francisco State University in 2004. His research is in combinatorics and number theory, in particular, counting integer points in polyhedra and the application of these enumeration functions to various mathematical topics and problems. He co-authored two books and about three scores of research papers and was honored and humbled by the 2012 teaching award of the MAA's Golden Section and the 2013 Haimo Award of the MAA.

Presentation Slides: PDF

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