Adam Kanigowski (University of Maryland) and Kosma Kasprzak (Jagiellonian University, Krakow)
Zoom link: https://univ-lille-fr.zoom.us/j/95130093232?pwd=U8j4u1gjbR5Zqwcvrkp39gI0OrqE4o.1
Speaker: Adam Kanigowski (University of Maryland)
Title: Ergodic Theorems along sparse subsets of the integers
Abstract: Let $A$ be a subset of the positive integers. For a dynamical system $(T,X)$ we are interested in ergodic averages along $A$, i.e. for $x\in X$ and $f\in C(X)$ we look at the limiting behavior of $\frac{1}{|A_N|}\sum_{k\in A_N}f(T^kx)$, where $A_N={k\in A: k\leq N}$.
We will focus on the case where $A$ is the set of primes or values of polynomials with integer coefficients. We will recall some classical results, mention some recent developments and highlight some interesting open problems.
Speaker: Kosma Kasprzak (Jagiellonian University, Krakow)
Title: Ergodicity along square orbits in rigid dynamical systems
Abstract: In this talk we will focus on topological dynamical systems exhibiting rigidity; that is, systems $(X, T)$ where some sequence of iterates $T^{q_n}$ approaches the identity function on $X$. It turns out, that a variant of this property gives us control over the ergodic averages along squares for any starting point $x\in X$. We will showcase this original result, discuss its proof and provide a class of examples of systems satisfying the assumptions.
Time and location:
Tue, 01 Oct 2024 16:00:00 UTC -
TBA
Zoom link: https://univ-lille-fr.zoom.us/j/95130093232?pwd=U8j4u1gjbR5Zqwcvrkp39gI0OrqE4o.1
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