# 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

Click on + iCal Export
or on
+ Google Calendar to add this event to your calendar.

**NOTE:** *The seminar will be streamed live on our YouTube
channel then saved there. If you ask questions, with your video feed
on or off, you agree to the use of your image/spoken words for said
purpose.*