The announcements are updated continuously. For a list of talks in the coming weeks, please see here.
Hebrew University Set Theory Seminar
Time: Wednesday, 12 June, 13:00-15:00 local time (12:00-14:00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Leeds Set Theory Seminar
Time: Wednesday, 12 June, 13:00-14:00 local time (14:00-15:00 CEST)
Speaker: Christopher Henney-Turner, Institute of the Polish Academy of Sciences
Title: Forcing Axioms and Name Principles
Abstract: We will study a class of forcing axioms called “name principles”. These say: “If sigma is a sufficiently nice name which is forced to have some property, then we can find a filter g in V such that sigma^g has that property.” It turns out that these name principles are deeply connected to one another, and to classical forcing axioms.
Information: Zoom link: https://universityofleeds.zoom.us/j/89414887798?pwd=SmRXMGwvUWkvYWptVUlnZHZpeFF5UT09
Caltech Logic Seminar
Time: Wednesday, 12 June, 12:00 – 13:00pm Pacific time (21:00 – 22:00 CEST)
Speaker: Jan Grebik, UCLA and Masaryk University
Title: Translational tilings of the plane by a polygonal set
Abstract: The periodic tiling conjecture (PTC) in Zd, that was recently disproved by Greenfeld and Tao, asserts that if a finite set F⊆Zd tiles Zd by translations, then it also tiles by (possibly different) translations that are periodic. On the other hand, the case d=2 has an affirmative answer which was proved earlier by Bhattacharya. The analogous question in R2 is open even for polygonal sets.
Here, the most general result is by Kenyon, who proved that PTC holds for topological disks. In an ongoing work with de Dios Pont, Greenfeld and Madrid, we obtain a structure result about translational tilings by polygonal sets with rational slopes by connecting the ideas from the discrete and continuous case. Our main result states that if such a tiling is topologically minimal, then it is weakly periodic and satisfies a weak version of PTC. In the talk I will discuss the main differences between tilings in Z2 and R2 as well as the main ideas how to apply the structure theory of Greenfeld and Tao in the continuous setting.
Information: See the seminar webpage.
Vienna Research Seminar in Set Theory
Time: Wednesday, 12 June, 15:00-16:30 CEST
Speaker: L. Notaro, University of Turin
Title: Does DC imply AC_\omega, uniformly?
Abstract: The axiom of dependent choice DC and the axiom of countable choice ACω are two weak forms of the axiom of choice that can be stated for a specific set: DC(X) assets that any total binary relation on X has an infinite chain; ACω(X) assets that any countable family of nonempty subsets of X has a choice function. It is well-known that DC implies ACω.
We discuss and sketch the proof of the following theorem: it is consistent with ZF that there is a set A⊆R such that DC(A)holds but ACω(A) fails.
This is joint work with Alessandro Andretta.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.
Vienna Research Seminar in Set Theory
Time: Thursday, 13 June, 11:30-13:00 CEST
Speaker: M. Eskew, Universität Wien
Title: Dense ideals (2/3)
Abstract: This is part of a three talk series. The first installment was on June 6.
In the second lecture, we will begin the consistency proof that all ωn can carry dense ideals simultaneously. We start with preliminaries on complete κ-closure, continuous projections, and inverse limits. Then we introduce our main forcing, the Dual Shioya collapse, and establish its key properties.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.
Vienna Logic Colloquium
Time: Thursday, 13 June, 15:00 – 15:50 CEST
Speaker: P. Speissegger, McMaster U, Hamilton
Title: How can model theory help understand Hilbert’s 16th problem?
Abstract: Hilbert’s 16th problem (the second part) states that the number of limit cycles of a polynomial vector field in the plane is bounded uniformly in the degree of the field. At first glance, this looks like a uniform finiteness statement, since the family of all polynomial vector fields of a fixed degree is definable in the real field. However, the corresponding family of limit cycles is not first-order definable in the real field; they are highly transcendental objects that can only be counted using something called Poincaré first-return maps.
I will explain a bit of the history of the problem and its supposedly easier cousin, Dulac’s problem (which only claims finiteness without the uniformity), and I will explain what these first-return maps are. Our conjecture is that these (families of) first-return maps are definable in some large o-minimal expansion of the real field. I will explain how this conjecture implies Dulac’s, and Hilbert’s 16th, problem, and I will give an idea of what we have managed to prove so far (with many collaborators who will be mentioned during the talk).
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.
European Set Theory Society 