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On pure-cycle Hurwitz number

Student-Run Algebraic Geometry Seminar

Speaker: Fu Liu, UC Davis
Location: 1147 MSB
Start time: Thu, Feb 9 2012, 1:10PM

Hurwitz numbers count branched covers of Riemann surfaces with prescribed branch type. This has an equivalent formulation in purely group theoretic terms, counting the number of tuples of permutations satisfying certain conditions. I will start by introducing the problem in both settings. We study the case where each branch point has only one ramified point over it, which corresponds to each permutation being a cycle. We present formulas in some special cases. This is based on joint work with Osserman and joint work with Du.