Dynamics Seminar

Event Information On small gaps in the length spectrum
13:10 on Wednesday October 23, 2019
14:00 on Wednesday October 23, 2019
BA6180, Bahen Center, 40 St. George St.
Dmitry Jakobson

McGill University

We discuss upper and lower bounds for the size of gaps in the length spectrum of negatively curved manifolds. For manifolds with algebraic generators for the fundamental group, we establish the existence of exponential lower bounds for the gaps. On the other hand, we show that the existence of arbitrary small gaps is topologically generic: this is established both for surfaces of constant negative curvature, and for the space of negatively curved metrics. While arbitrary small gaps are topologically generic, it is plausible that the gaps are not too small for almost every metric; we discuss one result This is joint work with Dima Dolgopyat.