# Category Archives: Seminars

## Clinton Conley: Unfriendly colorings of measure-preserving graphs of finite cost

Mathematical logic seminar – Jan 16 2018
Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         Clinton Conley
Department of Mathematical Sciences
CMU

Title:     Unfriendly colorings of measure-preserving graphs of finite cost

Abstract:

We show that any measure-preserving Borel graph on a standard probability space with finite average degree admits a Borel unfriendly coloring on a conull set. This generalizes the results for group actions discussed last semester, and is joint work with Omer Tamuz.

## Osvaldo Guzman Gonzalez: On (1,w_1)-weakly universal functions

Place: Fields Institute (Room 210)

Date: January 12, 2018 (13:30-15:00)

Speaker: Osvaldo Guzman Gonzalez

Title: On (1,w_1)-weakly universal functions

Abstract: We will study a very weak notion of universality of functions in Sacks models. We will answer a question of Shelah and Steprans by showing that there are no (1,w_1)-weakly universal functions after adding uncountably many Sacks reals side by side.

## 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.

## David Schrittesser – On the Complexity of Maximal Cofinitary Groups

Talk held by David Schrittesser (KGRC) at the KGRC seminar on 2018-01-11.

Abstract: A maximal cofinitary group is a subgroup of the group of permutations of the set of natural numbers $\mathbb N$ such that any group element has only finitely many fixed points, and no strictly larger group of permutations of $\mathbb N$ has this property. Improving a result of Horowitz and Shelah, we show that there is a closed maximal cofinitary group.

## 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.

## Omer Mermelstein: ​Searching for template structures in the class of Hrushovski ab initio geometries

BGU seminar in Logic, Set Theory and Topology.
Tuesday, ​December ​​​26th, 12:15-13:3, Seminar room -101, Math building 58.
Speaker:​ ​ Omer Mermelstein (BGU)

Title: ​​Searching for template structures in the class of Hrushovski ab initio geometries

Abstract. Zilber’s trichotomy conjecture, in modern formulation, distinguishes three flavours of geometries of strongly minimal sets — disintegrated/trivial, modular, and the geometry of an ACF. Each of these three flavours has a classic “template” — a set with no structure, a projective space over a prime field, and an algebraically closed field, respectively. The class of ab initio constructions with which Hrushovski refuted the conjecture features a new flavour of geometries — non-modular, yet prohibiting any algebraic structure.

In this talk we take a step towards defining “template” structures for the class of (CM-trivial) ab initio Hrushovski constructions. After presenting intuitively the standard ab initio Hrushovski construction, we generalize Hrushovski’s predimension function, showing that the geometries associated to certain Hrushovski constructions are, essentially, ab initio constructions themselves. If time permits, we elaborate on how these geometric structures may generate the class of geometries of ab initio constructions under the Hrushovski fusion operation.

## Omer Ben-Neria: Singular Stationarity and Set Theoretic Generalizations of Algebras

HUJI Logic Seminar

This Wednesday, 27 December, we will have a meeting of the Logic Seminar. The meeting will be in Ross 63 (notice room change) , 27 December (Wednesday), 11:00 – 13:00.

Speaker: Omer Ben-Neria
Title: Singular Stationarity and Set Theoretic Generalizations of Algebras
Abstract. The set theoretic generalizations of algebras have been introduced in the 1960s to give a set theoretic interpretation of usual algebraic structures. The shift in perspective from algebra to set theory is that in set theory the focus is on the collection of possible algebras and sub-algebras on specific cardinals rather than on particular algebraic structures. The study of collections of algebras and sub-algebras has generated many well-known problems in combinatorial set theory (e.g., Chang’s conjecture and the existence of small singular Jonsson cardinals).
In the 1990s Foreman and Magidor used algebras to initiate a study of Singular Stationarity, i.e., a study of alternative notions of stationarity for subsets of singular cardinals. They introduced and developed two notions of singular stationarity called Mutual Stationarity and Tight Stationarity, and used their findings to prove a fundamental result concerning generalized nonstationary ideals.
The two notions of singular stationarity have been studied in the last two decades, and the main purpose of the talk to describe the related known and recent results.
I will start by giving some background material on algebras and stationary sets, and describe the history of a well-known problem by Jonsson. We will then proceed to describe the work done on the notion of Mutually Stationary Sequences and sketch a recent proof which is based on the existence of special types of strong filters.
In the second part of the talk, we will connect the notions of Singular Stationarity to results from PCF theory and Extender-based forcing methods.

## Dan Nielsen : Mapping the Ramsey-like cardinals

Monday, December 18, 2017, 16.30
Seminar room 0.008, Mathematical Institute, University of Bonn

Speaker: Dan Nielsen (University of Bristol)

Title: Mapping the Ramsey-like cardinals

Abstract:

Ramsey-like cardinals were introduced in Gitman (2011) and Gitman & Welch (2011), broadly speaking being cardinals k that are critical points of elementary embeddings from a size k ZFC^- model. Recently, Holy & Schlicht (2017) have introduced a new large cardinal into the Ramsey-like family, called (strategic) alpha-Ramsey cardinals, whose distinctive feature is that they admit a game-theoretic characterisation. I will present some new results concerning how these Ramsey-like cardinals fit into the large cardinal hierarchy and how they interact with the core model K. This is joint work with Philip Welch.

## 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