Number Theory Seminar

Date: March 22, 2017

Time: 1:45PM - 2:45PM

Location: BLOC 220

Speaker: Michael Zieve, University of Michigan

Title: Uniform boundedness for maps between curves

Abstract: I will discuss the following conjecture: every rational map between curves over Q induces a map on rational points that is (<=32)-to-1 over all but finitely many values. In case the curves have genus one, this is a slightly weaker version of Mazur's uniform boundedness theorem. Progress towards the full result has relied on progress towards determining all possibilities for the monodromy group and ramification type of a complex rational function, contributing to problems originating in work of Zariski and Hurwitz.

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