University of Minnesota Combinatorics Seminar
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Abstract |
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Over the past 20 years, tantalizing analogies have emerged between the world of Riemann surfaces and the world of finite graphs. In this talk, I will discuss the role of symmetry groups in these analogies. In particular, I will present genus bounds for the maximal size of the relevant symmetry groups in both contexts, and discuss Hurwitz groups for surfaces and their analogue for graphs: these are the groups that achieve the upper genus bound for surfaces (or graphs, respectively). I will conclude by presenting a new result demonstrating an unexpected direct connection between finite graphs and Riemann surfaces -- the analogy is deeper than expected. |