Date: Wednesday, February 21, 2018
Location: 3866 East Hall (4:00 PM to 5:30 PM)
Title: The Ahlfors Measure Conjecture
Abstract: In 1966, Ahlfors conjectured that if the Lebesgue measure of the limit set of a Kleinian group is positive, then the limit set is the whole Reimann sphere. This conjecture was established by work of Canary in the geometrically finite case, and the general case follows from work of Agol. We will discuss Canary's proof in the geometrically finite case. We will then consider the corresponding statement for rational maps, which happens to be false. Indeed, in 2006, Buff and Cheritat proved that there are rational maps f, (specifically, quadratic polynomials), such that the Julia set J(f) has positive Lebesgue measure, but J(f) is not equal to the whole sphere.
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Speaker: Maxime Scott
Institution: Indiana University
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