Mobius disjointness for irregular flows

Abstract: 

The behavior of the Mobius function is central in the theory of prime numbers. A surprising connection with the theory of dynamical systems was discovered in 2010 by P. Sarnak, who formulated the Mobius Disjointness Conjecture (MDC), which asserts that the Mobius function is linearly disjoint from any zero-entropy flows. This conjecture opened the way into a large body of research on the interface of analytic number theory and ergodic theory. In this talk I will report how to establish MDC for a class of irregular flows, which are in general mysterious and ill understood. This is based on joint works with P. Sarnak, and with W. Huang and K. Wang.

This talk is part of the online Number Theory Web Seminar, and will be streamed live on Zoom.

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Organisers:

Mike Bennett (University of British Columbia)

Philipp Habegger (University of Basel)

Alina Ostafe (UNSW Sydney)