## Wednesday seminar: Andrew Brooke-Taylor

Dear all,

The seminar meets on Wednesday April 4th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

We will have a guest speaker Andrew Brooke-Taylor.

Best,
David

## Borisa Kuzeljevic: Isomorphic substructures of Fraisse limits

Dear all,

The seminar meets on Wednesday March 28th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Borisa Kuzeljevic — Isomorphic substructures of Fraisse limits

This is joint work with Milos Kurilic. For a relational structure X, its poset of copies is the set of all the substructures of X which are isomorphic to X, enlarged with the empty set, and ordered by inclusion. We will analyze posets of copies of various countable ultrahomogeneous structures. In particular, we will show that for many of these structures the class of order types of maximal chains of copies coincides with the class of order types of compact sets of reals with minimum non-isolated.

Best,
David

## Adam Bartoš: Compactifiable classes and Borel complexity up to the equivalence

The seminar meets on Wednesday March 7th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Adam Bartoš — Compactifiable classes and Borel complexity up
to the equivalence
We discuss the notion of compact composition of a class of metrizable
compacta, and a general question of compactifiability of a given class.
This is connected to the Borel complexity of subsets of the hyperspace
of all metrizable compacta, up to the equivalence of classes.

## Jan Grebik: Applications of topological dynamics to graphons

The seminar meets on Wednesday February 28th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Jan Grebik — Applications of topological dynamics to graphons
We show that the question about the existence of a Borel or continuous
lift for graphons has its counterpart in topological dynamics. We
present the optimal result in the general setting and then translate it
back to the original problem.

## Two talks: Aurichi and de Rancourt

The seminar meets on Wednesday February 7th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Time permitting, we will have two talks.

1. Leandro Aurichi — Some problems with products of Lindelöf spaces
Some problems about the preservation of the Lindelöf property on
products will be discussed.
2. Noé de Rancourt — Ramsey theory with and without pigeonhole principle
I will present an abstract infinite-dimensional Ramsey principle that doesn’t need any pigeonhole principle, and then I will compare the cases where the pigeonhole principle holds and the cases where it doesn’t, in a metamathematical way.

## Egbert Thümmel: Ramsey analytic ideals

The seminar meets on Wednesday January 17th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Egbert Thümmel — Ramsey analytic ideals
It is an open problem whether analytic tall ideals can be Ramsey. We
show that this is connected to another problem of Hrušák: If an analytic
tall Ramsey ideal exists, then it is nowhere Katětov above the ideal
conv and has no F-sigma extension.

## Dana Bartošová: Ellis problem for automorphism groups

The seminar meets on Wednesday January 10th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Dana Bartošová — Ellis problem for automorphism groups

Abstract: It is an old problem of Ellis to determine whether two
prominent dynamical system of a given topological group are isomorphic.
For discrete groups, only the integers are known to be a counterexample
by a complex result of Glasner and Weiss. Trivially, groups acting with
a fixed point under any action are counterexamples. We extend the class
of counterexamples to a few automorphism groups and we will have a
closer look at the full permutation group, $S_{\infty}$. This leads us
to questions about the existence of certain ultrafilters on natural
numbers. This is a joint work with Andy Zucker.

## Jan Grebik: Borel selector for Hypergraphons

The seminar meets on Wednesday January 3rd at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Jan Grebik — Borel selector for Hypergraphons
We recall all relevant definitions and show that there is a Borel way of
choosing a concrete representant of a hypergraphon.

## Jonathan Verner: Krom’s linearly ordered topological space which is not normal

Dear all,

The seminar meets on Wednesday 20th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program:
Jonathan Verner will deliver a short talk on the topic announced below.
There will probably be a enough time for one more talk, volunteer
speakers are welcome.

M. Krom: A linearly ordered topological space which is not normal

Recall that in an introductory course in topology one learns that every
linearly ordered topological space is normal. If the course is good, it
is also pointed out that the construction requires the axiom of choice.
In this talk we will present a nice construction, due to Melven Krom,
which uses a specific instance of the failure of AC to build a linearly
ordered topological space which is not normal. Krom’s construction
answered an, at the time, long standing open question of Birkhoff.

Best,
David

## Jonathan Verner: Coloring metric spaces

Dear all,

The seminar meets on Wednesday December 6th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program:
Jonathan Verner — Coloring metric spaces: A report from the oracle

“I will present a short and elegant argument, due to S. Shelah, showing how one can construct a metric space $X$ of size $2^\omega$ such that for any countable metric space  $K$ and any countable coloring of $X$ there is a monochromatic scaled copy of $K$ in $X$”.