Announcements are updated continuously on the website. For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2022.
KGRC Set Theory Seminar, Vienna
Time: Tuesday, 21 June, 15:00-16:30 CEST
Speaker: David Schrittesser, University of Toronto
Title: The Ramsey property, MAD families, and their higher dimensional relatives
Abstract: Infinite maximal almost disjoint families, dubbed “MAD families” by A.R.D. Mathias, have long been an object of interest in set theory, topology, and other areas. A question which has been tossed around for quite a while was whether there can exist an analytic Fin2-MAD family – that is, a two-dimensional variant of the usual notion of MAD family. Analytic (one-dimensional) MAD families cannot exist, so the conjecture has always been “no” – and indeed the answer is “no”, as was shown in joint work with Törnquist and Bakke Haga in 2016.
In 1969, Mathias asked whether Ramsey regularity rules out the existence of (one dimensional) MAD families. This question was answered positively in joint work with Törnquist in 2019.
But now that we know that Fin2 MAD families behave like MAD families in some respects, and that Ramsey regularity rules out (one dimensional) MAD families, does Ramsey regularity also rule out the two dimensional variant?
Yes, Ramsey regularity rules out the existence of Fin2 MAD families (also joint work with Asger Törnquist). The result even holds for J-MAD families, where J is an ideal in the smallest class containing the ideal of finite sets and closed under Fubini products. I will also report on work in progress with our student Severin Mejak.
Information: This talk will be given via Zoom. Please contact Richard Springer for information how to participate.
Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 22 June, 14:00-16:00 Israel Time (13:00-15:00 CEST)
Information: Contact Menachem Magidor or Omer Ben-Neria ahead of time for the seminar announcement and zoom link.
Barcelona Set Theory Seminar
Time: Wednesday, 22 June, 16:00-17:30 CEST
Speaker: Jeffrey Bergfalk
Title: Higher derived limits and higher dimensional partitions of partial orders
Abstract: This talk will primarily survey the recent work “A descriptive approach to higher derived limits”, joint with Nathaniel Bannister, Justin Moore, and Stevo Todorcevic (arXiv:2203.00165). At the heart of this work is a new family of partition principles which synthesize several recent advances in the study of higher derived limits, rendering those results far more amenable to combinatorial analyses. These principles admit formulation on any directed quasi-order, and are of particular, and interrelated, interest on the quasi-orders (ww, £*) and the ordinals wn. We’ll begin with a brief review of higher derived limits, then turn our attention to these partition principles, closing with a selection of open questions.
Information: Online. If you wish to attend, please send an email to firstname.lastname@example.org asking for the link.