Alternatively have a look at the program.

## Joint equidistribution within 4 modular surfaces and 2 spheres

We will discuss an equidistribution problem concerning rational planes in four-space. Due to an accidental isomorphism this problem relates in a natural manner to the simultaneous study of four CM-points on the modular surface and two points on the two-dimensional sphere. Using Duke's theorem and a joining classification we obtain joint equidistribution under suitable congruence conditions on the covolume of the planes.

This is joint work with Menny Aka and Andreas Wieser, and relies on a joint theorem with Elon Lindenstrauss.

## On the Liouville property of action of discrete groups

We will discuss the Liouville property of actions, relate it to amenability and to additive combinatorics

for certain classes of groups. One of the central part of the discussion will be Thompson group F.

We will discuss several open problems in additive combinatorics which relate to Liouville property of certain actions of Thompson group.

## Dynamics on abelian varieties in positive characteristic

We show that the dynamics of endomorphisms of abelian varieties (e.g., elliptic curves) over field of characteristic $p>0$ is sharply divided according to two possible scenario’s, reflected in properties of the Artin-Mazur zeta function (transcendental/rational) and orbit growth, somewhat similar to the mixing/non-mixing dichotomy in measurable dynamics. The two scenario’s are distinguished by the action on the $p$-torsion subgroup scheme.

## On the topology of integer polynomials with bounded coefficients

Let $q>1$ be a real number and $m\geq 1$ an integer. Let $Y$ denote the set of number $f(q)$ where $f$ runs over the integer polynomials with height not exceeding $m$. In this talk, we consider an old question when $Y$ is dense in the real line. This question is closely related to the studies of Bernoulli convolutions, beta-expansions and iterated functions systems. We prove the following conjecture of Erd\H{o}s et al.: $Y$ is dense if and only if $q$ is less than $m+1$ and is non-Pisot.

## Life and Mathematics of Sergiĭ Kolyada

Sergi

The first part of the talk will be devoted to important moments of his life. In the second part we will briefly discuss some of his scientific contributions to low dimensional and topological dynamics.

## Audience recollections of Sergiĭ Kolyada

## Special alpha-limit sets

This is an unfinished work, started last year with Sergiy Kolyada and

Lubomir Snoha. I hoped all three of us would complete it during this

meeting...

We investigate the notion of the special alpha-limit set of a point.

For a given map of a compact space to itself, it is defined as the

union of the sets of accumulation points over all backward branches of

the map. We consider mainly the case of interval maps. We give many

examples showing how those sets may look like. The main question is

## Rigid and rigid-like spaces in topological dynamics

A space is rigid if the only continuous selfmaps of this space are the constant maps and the identity. We show that rigid spaces, in fact so called Cook continua, can be used to produce spaces with nontrivial interesting dynamics. We also discuss `rigid-like' spaces in topological dynamics; as an application we get that the class of compact metric spaces admitting minimal maps is not closed with respect to products.

## Teichmuller curves mod $p$

A Teichmuller curve is a totally geodesic curve in the moduli space of Riemann surfaces. These curves are defined by polynomials with integer coefficients which are irreducible over $\mathbb C$. We will show that these polynomials have surprising factorizations mod $p$. This is joint work with Keerthi Madapusi Pera.

## Height pairings and preperiodic points in P^1

In 2011, Matt Baker and I used height functions and arithmetic equidistribution to show when two complex rational functions have only finitely many (pre-)periodic points in common. In this talk, I will explain how to obtain uniform bounds in families, inspired by questions and conjectures about elliptic curves and their torsion points. The key ingredient is an estimate on the Arakelov-Zhang intersection numbers in families of heights. This is joint work with Holly Krieger and Hexi Ye.

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