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Branched covers of the Riemann sphere and algebraic curves


Speaker: Brian Osserman, UC Berkeley
Location: 1147 MSB
Start time: Tue, Jan 23 2007, 4:10PM

We discuss new progress in a very classical field: the study of branched covers of the Riemann sphere. We first recall the classical picture as developed by Hurwitz, including the relationship between branched covers and group-theoretic monodromy data, and the Hurwitz spaces which parametrize branched covers. We then give two new results: a connectedness result, joint with Fu Liu, for certain Hurwitz spaces in the classical setting, and a result which can be viewed as an analogue of the Riemann existence theorem for certain tamely branched covers of the projective line.