Dynamics Lunch

The Dynamics Lunch seminar meets regularly on Tuesdays at 12:00 at the lobby of the Manchester building. Speakers talk not about their own work, but rather about some interesting paper they read (can be classical or new), that they think might be interesting to a broad dynamical audience (many times it is attended also by people from combinatorics/analysis/group theory). Meanwhile all attendants eat fruit and sandwiches. Dynamics lunch seminar

2018 Oct 23

Dynamics Lunch: Amir Algom "On \alpha \beta sets."

12:00pm to 1:00pm

Location: 

Manchester faculty club
Let $\alpha, \beta$ be elements of infinite order in the circle group. A closed set K in the circle is called an \alpha \beta set if for every x\in K either x+\alpha \in K or x+\beta \in K. In 1979 Katznelson proved that there exist non-dense \alpha \beta sets, and that there exist \alpha \beta sets of arbitrarily small Hausdorff dimension. We shall discuss this result, and a more recent result of Feng and Xiong, showing that the lower box dimension of every \alpha \beta set is at least 1/2.
2018 Jun 26

Dynamics Lunch: Jasmin Matz (Huji) ״Distribution of periodic orbits of the horocycle flow״

12:00pm to 1:00pm

Location: 

Manchester lounge
An old result of Hedlund tells us that there are no closed orbits for the horocycle flow on a compact Riemann surface M. The situation is different if M is non-compact in which case there is a one-parameter family of periodic orbits for every cusp of M. I want to talk about a result by Sarnak concerning the distribution of the such orbits in each of these families when their length goes to infinity. It turns out that these orbits become equidistributed in M and the rate of convergence can in fact be quantified in terms of spectral properties of the Eisenstein series on M.
2018 May 29

Dynamics Lunch: Matan Seidel (Huji) - "The Mass Transport Principle in Percolation Theory"

12:00pm to 1:00pm

Location: 

Manchester lounge
The Mass Transport Principle is a useful technique that was introduced to the study of automorphism-invariant percolations by Häggström in 1997. The technique is a sort of mass conservation principle, that allows us to relate random properties (such as the random degree of a vertex) to geometric properties of the graph. I will introduce the principle and the class of unimodular graphs on which it holds, as well as a few of its applications.

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