Continued Fractions, Interval Exchanges and Applications to Geometry
timetable:
Wed 12 Jun, 10:30 - 11:20, Aula Dini
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Some rank one interval exchanges satisfying both Sarnak and Veech
speaker: Sébastien Ferenczi (Institut de Mathématiques de Marseille, CNRS)abstract: We build examples of interval exchanges, for any number of intervals and any Rauzy class, satisfying Sarnak's conjecture on orthogonality with the Moebius function, and also the old ergodic conjecture on simplicity (stated by Veech as a question). We use a criterion of Bourgain, which proves Sarnak's conjecture through symbolic properties of the system, linked to its generation by Rokhlin towers, and these can be obtained by the new renormalization process on interval exchanges known as the self-dual induction, or its generalization outside the hyperelliptic class. Then simplicity is reached through isomorphism with a variant of the Del Junco-Rudolph rank one map.
timetable:
Wed 12 Jun, 10:30 - 11:20, Aula Dini
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