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Counting the number of representations of a surface group


Speaker: Motohico Mulase, UC Davis
Location: 693 Kerr
Start time: Wed, Oct 9 2002, 4:10PM

Let G be an arbitrary finite group and S a closed surface. In this talk I will give an elementary proof of an amazing formula that gives the number of homomorphisms from the fundamental group of S into G. For an oriented Riemann surface S, the formula reduces to the result of Freed and Quinn (CMP 93). For a non-orientable surface, our formula seems to be new (so far). The formula was originally discovered by matrix integral theory (math.QA/0209008), but the proof given in this talk is completely elementary. The talk is based on joint work with Josephine Yu. (If time permits, an extension of the theory to compact groups may be discussed.)