Department of Mathematics

Prof. Dr. Mariusz Lemańczyk, Nikolaus-Kopernikus Universität Toruń: "Sarnak's conjecture on Möbius disjointness - first steps"

Nov 05, 2018 from 04:15 PM to 06:00 PM

LMS 4 - Raum 312 - Diskussionsraum

Abstract:

I plan to present an introduction to joining theory and some topological dynamics with an illustation of so-called square-free systems. The square-free system is a factor of the main object which we intend to study: the Möbius subshift. The Chowla conjecture on corellations of the Möbius function will be presented, and I plan to show why the Chowla conjecture is a purely ergodic statement on the Möbius subshift. The main aim will be to show that the Chowla conjecture implies Sarnak's conjecture by using joinings. Finally, I plan to show how some number-theoretic properties  of arithmetic functions should be ''read'' in ergodic theory language.

 

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