Lecture----数学院晨兴数学中心

Title:	A uniform boundedness conjecture for rational functions
Speaker:	Professor Michael Zieve (University of Michigan)
Time:	2016-12-27, 16:00-17:00
Place:	610
Abstract:	I will explain the progress that has been made towards proving the following conjecture: there is an absolute constant N such that the function f : P^1(Q)-->P^1(Q) induced by any f(x) in Q(x) is (<=N)-to-1 over all but finitely many points. The key point here is that N is independent of f. This conjecture is a vast generalization of the uniform boundedness of rational torsion on elliptic curves (Mazur's theorem). Work on this conjecture has led to progress on both Hurwitz's existence problem (describing the ramification types of rational functions) and Zariski's thesis problem (describing the monodromy groups of rational functions).
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