# Online activities 27 March – 2 April

The announcements are updated continuously. For a list of talks in the coming weeks, please see here.

Vienna Research Seminar in Set Theory
Time: Tuesday, 28 March, 15:00-16:30 CEST
Speaker: Miguel Moreno, Universität Wien
Title: Generalised Descriptive Set Theory, part III
Abstract: Following part I and part II in this three part series, during this talk we will discuss where in the generalized Borel-reducibility hierarchy are the isomorphism relation of first order complete theories. These theories are divided into two kinds: classifiable and non-classifiable. To study the classifiable theories case is needed the use of Ehrenfeucht-Fraïssé games. On the other hand the study of the non-classifiable theories is done by using colored ordered trees. The goal of the talk is to see the classifiable theories case and sketch the ideas of non-classifiable theories.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

Baltic Set Theory Seminar
Time: Tuesday, 28 March, 15:00-16:30 CEST
Speaker: Several
Title: Baltic Set Theory Seminar
Abstract: This is a learning seminar, the goal is to actually go over proofs and more or less understand them. Discussions are encouraged. The topic of the seminar is the following:
1. Sandra Müller, Stationary-tower-free proof of Woodin’s Sealing Theorem.
2. Matteo Viale, Generic absoluteness theorem for the omega_1 Chang model conditioned to MM^{+++}.
Information: Please see the seminar webpage.

CMU Logic Seminar
Time: Tuesday, 28 March, 3:30 – 4:30pm Pittsburgh time (21:30 – 22:30 CEST)
Speaker: Matthieu Joseph, Université Paris Saclay
Title: Several notions of freeness for actions of countable groups
Abstract: In this talk we will study different notions of freeness for actions of countable groups by homeomorphisms on compact spaces. Genuine freeness, freeness in the sense of (some) invariant measure and freeness in the sense of the topology will be compared, via concrete examples. We will bring out and discuss the class of allosteric groups, which is the class of groups that admit actions on compact spaces with an invariant measure that are free in the sense of the topology but non-free in the sense of the measure.
Information: See the seminar webpage.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 29 March, 13:00-15:00 Israel Time (12:00-14:00 CET)
Speaker: Yair Hayut
Title: Sealing Kurepa trees
Abstract: In this talk, I’m going to describe Itamar Giron’s master thesis. Most of the results in this talk are due to him.
The main question of the thesis was whether there is a forcing notion that makes an arbitrary Kurepa tree into a non-distributive one, and how far can one go in this direction (can we get sealed Kurepa trees?).
We will start with the classical construction of a Kurepa tree in L (by Solovay). We will show that this tree is distributive in L. We will review the known constructions due to Poor and Shelah (generalized by Muller and me), of sealed Kurepa trees in L (can be generalized to canonical inner models).
Then, we will also find a forcing extension in which for every Kurepa tree, one can add a branch without collapsing cardinals.  This means that even though it is easy to find non-distributive Kurepa trees, it is far less trivial to get from combinatorial assertions (such as diamond*), a sealed Kurepa tree.
Finally, I will talk about the forcing notion that “specializes” a Kurepa tree over an arbitrary model of ZFC. This is Giron’s main result, which requires the most sophisticated tools.
Information: Contact Menachem Magidor or Omer Ben-Neria ahead of time for the zoom link.

Vienna Logic Colloquium
Time:
Thursday, 30 March, 15:00 – 15:45 CET
Speaker: M. Pinsker, TU Wien
Title: Constraint Satisfaction Problems: algebraic and model-theoretic challenges to distinguish the easy from the hard
Abstract: I will give a gentle introduction to current algebraic and model-theoretic methods in the computational complexity of Constraint Satisfaction Problems (CSPs).
A CSP is a computational problem where we are given variables and constraints about them; the question is whether the variables can be assigned values such that all constraints are satisfied. Numerous natural computational problems, such as satisfiability of a given system of equations over a field, are CSPs; in fact, any computational problem is Turing-equivalent to a CSP.
Any CSP can be modeled by a relational structure, and conversely every relational structure naturally defines a CSP. In view of humanity’s continuing quest to distinguish easy from hard problems in general, and the class P (polynomial-time solvable problems, e.g. satisfiability of linear equations over a field) from the class NP (polynomial-time verifiable problems, e.g. satisfiability of a propositional formula) in particular, the question arises which mathematical properties of a relational structure make the corresponding CSP easy and which make it hard. It turns out that particular algebraic invariants of the structure often determine the borderline between different complexity classes. Hence algebraic methods, combined with concepts from model theory as well as from Ramsey theory in the case of infinite structures, yield appropriate tools to determine the computational complexity of CSPs.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

Cross-Alps Logic Seminar
Time: Friday, 31 March, 16.00-17.00 CEST
Speaker: L. Patey, CNRS
Title: Canonical notions of forcing in Reverse Mathematics
Abstract: In Reverse Mathematics, a proof of non-implication from a statement P to a statement Q consists of creating a model of P which is not a model of Q. To this end, one usually create a complicated instance I of Q, and then, build iteratively a model of P containing I while avoiding every solution to I. The difficult part consists in building solutions to instances of P which will not compute any solution to I. This is usually done by forcing. Moreover, by some empirical observation, the notion of forcing used in a separation of P from Q usually does not depend on Q. For example, constructing models of WKL is usually done by forcing with Pi^0_1 classes. This tends to show that P admits a “canonical” notion of forcing. In this talk, we provide a formal framework to discuss this intuition, and study the canonical notions of forcing associated to some important statements in Reverse Mathematics. This is a joint work with Denis Hirschfeldt.
Information: The event will stream on the Webex platform. Please write to  luca.mottoros [at] unito.it  for the link to the event.

CUNY Set Theory Seminar
Time: Friday, 31 March, 12:15pm New York time (18:15 CET)
Speaker: Benjamin Goodman, CUNY
Title: Σn-correct forcing axioms
Abstract: The standard method of producing a model of a forcing axiom from a supercompact cardinal in fact gives a model of an even stronger principle: that for every small name a and every Σ2 formula arphi such that φ(a) is forceable by and preserved under further forcing in our forcing class, there is a filter F which meets a desired collection of dense sets and also interprets a such that φ(aF) already holds. I will show how to generalize this result to formulas of higher complexity by starting with slightly stronger large cardinal assumptions, then discuss the bounded versions of these enhanced forcing axioms, their relationships to other similar principles, and their consequences.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Toronto Set Theory Seminar
Time: Friday, 31 March, 1.30-3.00 Toronto time (19.30-21.00 CET)
Speaker: tba
Title: tba
Abstract: tba

CUNY Logic Workshop
Time: Friday, 31 March, 2:00 – 3:30 New York time (20:00-21:30 CET)
Speaker: Corey Switzer, University of Vienna
Title: tba
Abstract: tba
Information: The talk will take place in person. For more information, please see the seminar webpage or email Victoria Gitman.

# Bourbaki Seminars 31 March and 1 April

Please find below the program of the next Friday’s Bourbaki Seminar (31 March 2023) and Bourbaki Seminar (1 April 2023).

Links for the broadcasted talks will be available on the official webpage

https://www.bourbaki.fr/seminaires/2023/index.html#seminaire

just next to the title of each seminar [Live IHP].

__________________________________________________________________________

Séminaire Bourbaki du vendredi
Friday 31 March 2023
The Séminaire Bourbaki du vendredi takes place in the Institut Henri Poincaré.

14h — Romain Tessera: introduction aux cônes asymptotiques

15h — Mirna Džamonja: Les axiomes de forcing

16h30 — Maxime Bourrigan: Homologie de Morse et simplicité de groupes de transformations

___________________________________________________________________________

Séminaire Bourbaki
Saturday 1 April 2023
The Séminaire Bourbaki takes place in the Institut Henri Poincaré.

10h — Jonathan Hickman: Pointwise convergence for the Schrödinger equation, after Xiumin Du and Ruixiang Zhang

11h30 — Matteo Viale: Strong forcing axioms and the continuum problem, following Aspéro’ and Schindler’s proof that $\mathbf{MM}^{++}$ implies Woodin’s Axiom $(*)$

14h30 — Clara Löh:  Exponential growth rates in hyperbolic groups, after Fujiwara and Sela

16h — Étienne Ghys: Le groupe des homéomorphismes de la sphère de dimension~$2$ qui respectent l’aire et l’orientation n’est pas un groupe simple, d’après  D. Cristofaro-Gardiner, V. Humilière et S. Seyfaddini

__________________________________________________________________________

The next session of the séminaires will be held on Friday 23 and Saturday 24 June 2023.

# Online activities 20-26 March

The announcements are updated continuously. For a list of talks in the coming weeks, please see here.

Vienna Research Seminar in Set Theory
Time: Tuesday, 21 March, 15:00-16:30 CEST
Speaker: Miguel Moreno, University of Vienna
Title: Generalised Descriptive Set Theory, part II
Abstract: We have introduced the notions of K-Borel class, K-analytic class, K-analytic-coanalytic class, K-Borel* class in the previous talk. In descriptive set theory the Borel class, the analytic-coanalytic class, and the Borel* class are the same class, we showed that this doesn’t hold in the generalized descriptive set theory.
In this talk, we will show the consistency of “K-Borel* class is equal to the K-analytic class”. This was initially proved by Hyttinen and Weinstein (former Kulikov), under the assumption V=L. We will show a different proof that shows that this holds in L but also can be forced by a cofinality-preserving GCH-preserving forcing from a model of GCH, but also by a <κ-closed κ+‑cc forcing.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

Baltic Set Theory Seminar
Time: Tuesday, 21 March, 15:00-16:30 CEST
Speaker: Several
Title: Baltic Set Theory Seminar
Abstract: This is a learning seminar, the goal is to actually go over proofs and more or less understand them. Discussions are encouraged. The topic of the seminar is the following:
1. Sandra Müller, Stationary-tower-free proof of Woodin’s Sealing Theorem.
2. Matteo Viale, Generic absoluteness theorem for the omega_1 Chang model conditioned to MM^{+++}.
Information: Please see the seminar webpage.

CMU Core Model Theory Seminar
Time: Tuesday, 21 March, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CET)
Speaker:  Benjamin Siskind, Carnegie Mellon University
Title: The short extender of the Martin measure
Abstract: Under AD, using the uniform cofinalities analysis on function from finite products of omega_1 into omega_1, we show that the short extender of the the Martin measure ultrapower comes from the iterated ultrapower by the club filter on omega_1 and discuss some applications. We’ll also give an iterated ultrapowers proof of the uniform cofinality analysis. (We suspect that these observations have been noticed before but don’t know a reference.)

Leeds Models and Sets Seminar
Time: Wednesday, 22 March, 13:45-15:00 local time (14:45-16:00 CET)
Speaker: Bea Adam-Day, University of Leeds
Title: Indestructibility and $C^{(n)}$-supercompact cardinals
Abstract: In the 70’s Laver showed that a supercompact cardinal $\kappa$ may be made indestructible by a suitable class of forcings—namely, after a preparatory forcing, the supercompactness of $\kappa$ will not be destroyed by any further $<\kappa$-directed closed forcing. Many indestructibility results have since been written, as well as those demonstrating the impossibility of indestructibility (or even preservation) of many large cardinals. In this talk we will consider the case of $C^{(n)}$-supercompact cardinals—a stronger and more slippery variant of supercompact cardinals—and how they can be made indestructible for $n\leq 2$.
Information: Please see the seminar webpage.

Bristol Logic and Set Theory Seminar
Time: Wednesday, 22 March, 2-3.30 UK time (15.00-16.30 CET)
Speaker: Juan Aguilera, University of Ghent
Title: A generalization of Borel determinacy
Abstract: We present a theorem which is, in some sense, the provably optimal generalization of Martin’s Borel determinacy for infinite games on integers.

Toronto Set Theory Seminar
Time: Friday, 24 March, 1.30-3.00 Toronto time (19.30-21.00 CET)
Speaker: tba
Title: tba
Abstract: tba

CUNY Logic Workshop
Time: Friday, 24 March, 2:00 – 3:30 New York time (20:00-21:30 CET)
Speaker: Victoria Gitman, CUNY
Title: Parameter-free comprehension in second-order arithmetic
Abstract: Second-order arithmetic has two types of objects: numbers and sets of numbers, which we think of as the reals. The second-order arithmetic framework has been used successfully to investigate what kinds of real numbers need to exist to prove various significant results in analysis. One of the strongest second-order arithmetic axiomatizations is the theory Z2 consisting of the axioms PA (for numbers), the set induction axiom, and comprehension for all second-order formulas with set parameters. How significant is the inclusion of set parameters in the comprehension scheme? Let Z−p2 be like Z2, but where set parameters are not allowed in the comprehension scheme. Harvey Friedman showed that Z2 and Z−p2 are equiconsistent because parameter-free comprehension suffices to build a model’s version of the constructible universe L inside the model and the ‘constructible’ reals satisfy Z2. Kanovei recently showed that models of Z−p2 can be very badly behaved, for example, their sets may not even be closed under complement. Kanovei also showed that there can be nicely behaved models of Z−p2 in which Σ12-comprehension (with set parameters) holds. He constructed his model in a forcing extension by a tree iteration of Sacks forcing. In Kanovei’s model, Σ14-comprehension (with set parameters) fails and he asked whether this can be improved to Σ13-comprehension. In this talk, I will show how to construct a model of Σ12-comprehension and Z−p2 in which Σ13-comprehension fails. The model will be constructed in a forcing extension by a tree iteration of Jensen’s forcing. Jensen’s forcing is a sub-poset of Sacks forcing constructed by Jensen to show that it is consistent to have a non-constructible Π12-definable singleton real (every Σ12-definable set of reals is constructible by Shoenfield’s Absoluteness).
Information: The talk will take place in person. For more information, please see the seminar webpage or email Victoria Gitman.

# Fields Institute Lectures by Stevo Todorcevic, March 15-17

Stevo Todorcevic will give a series of three talks on solving basis problems by expanding mathematical structures on March 15, 16 and 17, 2023, each from 4 to 5 pm Eastern time (21.00-22.00 CET).  Details including the abstract can be found here: http://www.fields.utoronto.ca/activities/22-23/Stevo-Todorcevic

The talks will be in Fields Room 230, but also available on Zoom. If you are planning to attend, then you should register here: https://www.fields.utoronto.ca/cgi-bin/register?form_selection=set. For those planning to attend online, the Fields should email you the zoom link after you register.  Please email Spencer Unger if you have any problems with this.

# Online activities 13 – 19 March

The announcements are updated continuously. For a list of talks in the coming weeks, please see here.

Vienna Research Seminar in Set Theory
Time: Tuesday, 14 March, 15:00-16:30 CEST
Speaker: Miguel Moreno, University of Vienna
Title: Generalised Descriptive Set Theory, part I
Abstract: This is the first of three talks about Generalised Descriptive Set Theory. The aim of this talk is to introduce the notions of K‑Borel class, K‑analytic class, K‑analytic-coanalytic class, K‑Borel* class, and show the relation between these classes.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

Baltic Set Theory Seminar
Time: Tuesday, 14 March, 15:00-16:30 CEST
Speaker: Several
Title: Baltic Set Theory Seminar
Abstract: This is a learning seminar, the goal is to actually go over proofs and more or less understand them. Discussions are encouraged. The topic of the seminar is the following:
1. Sandra Müller, Stationary-tower-free proof of Woodin’s Sealing Theorem.
2. Matteo Viale, Generic absoluteness theorem for the omega_1 Chang model conditioned to MM^{+++}.
Information: Please see the seminar webpage.

CMU Core Model Theory Seminar
Time: Tuesday, 14 March, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CET)
Speaker: Dominik Adolf, University of North Texas
Title: Rudin-Keisler Capturing and Mutual Stationarity at successors of singulars
Abstract: Mutual Stationarity, first introduced by Foreman and Magidor, is a key concept for the study of stationary subsets on the powersets of singular cardinals. In this talk we will introduce a new way to add sequences with strong mutual stationarity properties by forcing. Towards this end we introduce a concept we dubbed Rudin-Keisler Capturing, a new large cardinal property living in the gaps of the Mitchell-Order. This is joint work with Omer Ben-Neria.

CMU Logic Seminar
Time: Tuesday, 14 March, 3:30 – 4:30pm Pittsburgh time (21:30 – 22:30 CEST)
Speaker: Alejandro Poveda Ruzafa, Harvard University
Title: The Gluing Property
Abstract: In this talk, I’ll report on a recent joint project with Y. Hayut where we introduce a new compactness principle called ‘’The Gluing Property’’. This concept was isolated from a former argument by Gitik saying that the existence of a \kappa-compact cardinal entails an inner model with a strong cardinal. During the talk, we shall introduce the gluing property and show that compact-like cardinals (such as strong compacts, \Pi^1_1-subcompacts, etc) do satisfy a certain amount of gluing. Contrarily, non-compact cardinals like strong cardinals are known to fail to have the gluing property. We shall conclude the exposition by discussing how to force the \omega gluing property from optimal assumptions. This latter being surprisingly mild – just “\exists \kappa (o(\kappa)=\omega_1)”.
Information: See the seminar webpage.

Vienna Logic Colloquium
Time:
Thursday, 16 March, 15:00 – 15:45 CET
Speaker: Silvain Rideau-Kikuchi, University of Paris
Title: Multi topological fields, approximations and NTP2
Abstract: (Joint work with S. Montenegro)
The striking resemblance between the behaviour of pseudo-algebraically closed, pseudo real closed and pseudo p-adically fields has lead to numerous attempts at describing their properties in a unified manner. In this talk I will present another of these attempts: the class of pseudo-T-closed fields, where T is an enriched theory of fields. These fields verify a «local-global» principle with respect to models of T for the existence of points on varieties. Although it very much resembles previous such attempts, our approach is more model theoretic in flavour, both in its presentation and in the results we aim for.
The first result I would like to present is an approximation result, generalising a result of Kollar on PAC fields, respectively Johnson on Henselian fields. This result can be rephrased as the fact that existential closeness in certain topological enrichments come for free from existential closeness as a field. The second result is a (model theoretic) classification result for bounded pseudo-T-closed fields, in the guise of the computation of their burden. One of the striking consequence of these two results is that a bounded perfect PAC field with n independent valuations has burden n and, in particular, is NTP2.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate

Cross-Alps Logic Seminar
Time: Friday, 17 March, 16.00-17.00 CEST
Speaker: Victor Selivanov, Institute of Informatics Systems, Novosibirsk
Title: Boole vs Wadge: comparing basic tools of descriptive set theory
Abstract: We systematically compare ω-Boolean classes and Wadge classes, e.g. we complement the result of W. Wadge that the collection of non-self-dual levels of his hierarchy coincides with the collection of classes generated by Borel ω-ary Boolean operations from the open sets in the Baire space. Namely, we characterize the operations, which generate any given level in this way, in terms of the Wadge hierarchy in the Scott domain. As a corollary, we deduce the non-collapse of the latter hierarchy. Also, the effective version of this topic and its extension to k-partitions are developed.
Information: The event will stream on the Webex platform. Please write to  luca.mottoros [at] unito.it  for the link to the event.

CUNY Set Theory Seminar
Time: Friday, 17 March, 12:15pm New York time (18:15 CET)
Speaker: Jonathan Osinski, University of Hamburg
Title: Model-Theoretic Characterizations of Weak Vopěnka’s Principle
Abstract: It has been known since the 1980s that Vopěnka’s Principle (VP) is equivalent to certain statements about logics, e.g. to the schema ‘Every logic has a compactness cardinal.’ On the other hand, it was only recently shown by Trevor Wilson that a related statement statement called Weak Vopěnka’s Principle (WVP) is strictly weaker than VP. In fact, Joan Bagaria and Wilson showed that WVP is equivalent to the existence of Πn-strong cardinals for all natural numbers n. We generalize logical characterizations of strong cardinals to achieve a characterization of Πn-strong cardinals and therefore of WVP in terms of properties of strong logics. This is partly joint work with Will Boney and partly with Trevor Wilson.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

CUNY Logic Workshop
Time: Friday, 17 March, 2:00 – 3:30 New York time (20:00-21:30 CET)
Speaker: Filippo Calderoni, Rutgers University
Title: Rotation equivalence and rigidity
Abstract: The theory of countable Borel equivalence relations analyzes the actions of countable groups on Polish spaces. The main question studied is how much information is encoded by the corresponding orbit space. The amount of encoded information reflects the extent to which the action is rigid.
In this talk we will discuss rigidity results for the action of the group of rational rotations. In particular we will analyze the rotation equivalence on spheres in higher dimension. This is connected to superrigidity results of Margulis and to Zimmer’s program about the actions of discrete subgroups of Lie groups on manifolds.
Information: The talk will take place in person. For more information, please see the seminar webpage or email Victoria Gitman.

Toronto Set Theory Seminar
Time: Friday, 17 March, 1.30-3.00 Toronto time (19.30-21.00 CET)
Speaker: George Domat
Title: Big Mapping Class Groups in Dimensions 0,1, and 2
Abstract: I’ll first give a broad introduction to big mapping class groups and why they may be of interest to set theorists. These groups are a rich class of non-archimedean Polish groups coming from the worlds of low-dimensional topology and geometric group theory. After this broad overview I will talk in more detail about some results (in parts joint with Mladen Bestvina, Ryan Dickmann, and Kasra Rafi) around automatic continuity properties of big mapping class groups of surfaces.

# New Perspectives in Pure Mathematics, Bristol 27-29 March

Registration is now open for our conference ‘New Perspectives in Pure Mathematics’. It will take place over three days, from 27th-29th March 2023. The conference website (with a link for registration) is below:

https://eur.cvent.me/DkaMq?RefId=Host

Registration closes on 12th March 2023.

We have an excellent line-up of speakers:

Andrew Granville (Montréal)
Ben Green (Oxford)
Scott Harper (St Andrews)
Alessandra Iozzi (ETH Zurich)
Franziska Jahnke (Muenster)
Tali Kaufman (Bar-Ilan)
Autumn Kent (Wisconsin)
Jungwon Lee (Warwick)
Shoham Letzter (UCL)
Menachem Magidor (Jerusalem)
Irene Pasquinelli (Bristol)
Ross Paterson (Bristol)
Michael Rathjen (Leeds)
Aner Shalev (Jerusalem)
Donna Testerman (EPFL)

We envisage that all but one of the talks will be in-person, and the talks (which span combinatorics, number theory, algebra, geometry and logic) should be accessible to a broad pure-mathematical audience. A programme can be found on the website linked to above.

Lunch will be provided each day, as well as tea and coffee, and there will be a wine reception on the Monday evening.

Best wishes,

Kentaro Fujimoto, on behalf of the organisers, David Ellis and Celine Maistret

# Online activities 6 – 12 March

The announcements are updated continuously. For a list of talks in the coming weeks, please see here.

Vienna Research Seminar in Set Theory
Time: Tuesday, 7 March, 15:00-16:30 CEST
Speaker: Juris Steprāns, York University
Title: Selective and Milliken-Taylor ultrafilters
Abstract: I will report on joint work with Dilip Raghavan solving a question of Blass about whether the existence of many selective ultrafilters implies the existence of Milliken-Taylor ultrafilters. The first part of the talk will provide the historical context of what was known in the mid 80s that prompted Blass to ask his question. The second part will discuss the key technical advance in our argument.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

Baltic Set Theory Seminar
Time: Tuesday, 7 March, 15:00-16:30 CEST
Speaker: Several
Title: Baltic Set Theory Seminar
Abstract: This is a learning seminar, the goal is to actually go over proofs and more or less understand them. Discussions are encouraged. The topic of the seminar is the following:
1. Sandra Müller, Stationary-tower-free proof of Woodin’s Sealing Theorem.
2. Matteo Viale, Generic absoluteness theorem for the omega_1 Chang model conditioned to MM^{+++}.
Information: Please see the seminar webpage.

Caltech Logic Seminar
Time: Tuesday, 7 March, 11:00am-12:00pm Pacific time (20:00-21:00 CET)
Speaker: Martino Lupini, University of Bologna
Title: Definable refinements of classical algebraic invariants
Abstract: In this talk I will explain how methods from logic allow one to construct refinements of classical algebraic invariants that are endowed with additional topological and descriptive set-theoretic information. This approach brings to fruition initial insights due to Eilenberg, Mac Lane, and Moore (among others) with the additional ingredient of recent advanced tools from logic. I will then present applications of this viewpoint to invariants from a number of areas in mathematics, including operator algebras, group theory, algebraic topology, and homological algebra.
Information: Please see the seminar webpage.

Leeds Models and Sets Seminar
Time: Wednesday, 8 March, 13:45-15:00 local time (14:45-16:00 CET)
Speaker: Soinbhe Nic Dhonncha, Manchester University
Title: Purity in chains of modules
Abstract: The model theory of modules extends naturally to certain functor categories. One such category is that of representations of the biinfinite quiver A_{\infty}^{\infty}, where each object can be thought of as a biinfinite chain of R-modules. This raises the question of how the objects and morphisms of (model theoretic) interest for this category relate to those of Mod R. In the simplest case, we take R to be von Neumann regular.
Information: Please see the seminar webpage.

Barcelona Set Theory Seminar
Time: Wednesday, 8 March, 16:00-17:30 CET
Title: Compactness principles at small cardinals and their preservation
Abstract: It is known that if k is a (typical) large cardinal and P is a forcing notion of size < k, then k is preserved as a large cardinal in the forcing extension V[P]. If k is a successor cardinal, for instance w2, and satisfies some compactness principles such the tree property or stationary reflection, the preservation of these compactness properties by forcing notions is more complicated. We will survey recent results in this area and focus on the result that over models of PFA, Cohen forcing at w of any length preserves the tree property at w2 and the negation of the weak Kurepa hypothesis at w1.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Bristol Logic and Set Theory Seminar
Time: Wednesday, 8 March, 16:30-17:30 UK time (17:30-18:30 CET)
Speaker: Minh Tran, University of Oxford
Title: Toward classifying the reducts of the complex fields
Abstract: We will discuss some recent progress on the problem of classifying the reducts of the complex field (with named parameters and up to interdefinability). The tools we use include the recent solutions of the Restricted Trichotomy Conjecture in characteristic 0 and a generalized sumproduct result from additive combinatorics. (Joint with Benjamin Castle)

CUNY Set Theory Seminar
Time: Friday, 10 March, 12:15pm New York time (18:15 CET)
Speaker: James Holland, Rutgers University
Title: Forcing more choice over the Chang model
Abstract: The ordinal Θ has lots of interesting results in the context of L(R). Here, we try to find an analogue of Θ for the Chang model, and see what assumptions about it are natural. These assumptions come out of the process of forcing more dependent choice over the Chang model.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Toronto Set Theory Seminar
Time: Friday, 10 March, 1.30-3.00 Toronto time (19.30-21.00 CET)
Speaker: Natasha Dobrinen, University of Notre Dame
Title: tba
Abstract: tba

# BLAST 2023, May 16 – 20

We would like to bring your attention to the upcoming BLAST 2023 conference, which will take place at the University of North Carolina, Charlotte, from May 16 – 20.

BLAST is a conference series focusing on Boolean Algebras, Lattices, Universal Algebra and Model Theory, Set Theory, and Topology. We hope that you will be able to attend the conference, and to contribute a talk.

The confirmed invited speakers for the conference are:
– Marco Abbadini, University of Salerno
– Dana Bartošová, University of Florida
– William Chan, University of North Texas
– Daniel Herden, Baylor University
– Andre Kornell, Dalhousie University
– David Stanovský, Charles University

Additionally, we can confirm that a tutorial will be given by:
– Keith Kearnes, University of Colorado Boulder

The website for this conference is still under construction, but a preliminary version can be found here: https://pages.charlotte.edu/blast2023/. The home website for the BLAST conference series can be found here: https://math.colorado.edu/blast/. Some financial support, provided by the National Science Foundation, is available for students and young researchers. Please do not hesitate to contact me if you have any questions. We hope that you will be able to join us in Charlotte this May. Until then,

Will Brian (wbrian.math@gmail.com)
on behalf of the conference organizers

# Online activities 27 February – 5 March

The announcements are updated continuously. For a list of talks in the coming weeks, please see here.

Baltic Set Theory Seminar
Time: Tuesday, 28 February, 15:00-16:30 CEST
Speaker: Several
Title: Baltic Set Theory Seminar
Abstract: This is a learning seminar, the goal is to actually go over proofs and more or less understand them. Discussions are encouraged. The topic of the seminar is the following:
1. Sandra Müller, Stationary-tower-free proof of Woodin’s Sealing Theorem.
2. Matteo Viale, Generic absoluteness theorem for the omega_1 Chang model conditioned to MM^{+++}.
Information: Please see the seminar webpage.

CMU Core Model Theory Seminar
Time: Tuesday, 28 February, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CET)
Speaker:  Gabriel Goldberg, University of California, Berkeley
Title: Inner models from stationary logic, part 3
Abstract: We discuss the inner model C(aa) introduced by Kennedy-Magidor-Väänänen, and answer several questions posed in their paper  “Inner models from strong logics”. Assuming large cardinal axioms, we’ll show that this model satisfies GCH (this is joint work with John Steel) and that C(aa) satisfies o(κ) = κ++ for all regular cardinals κ > ω1 (this is joint work with Otto Rajala).

Caltech Logic Seminar
Time: Tuesday, 28 February, 11:00am-12:00pm Pacific time (20:00-21:00 CET)
Speaker: Julien Melleray, Université Lyon 1
Title: Clopen type semigroups of actions on 0-dimensional compact spaces
Abstract: Consider an action of a discrete group G on a compact, 0-dimensional space X. Its clopen type semigroup is an algebraic structure which encodes the equidecomposability relation between clopen subsets of X (two clopen subsets A,B of X are equidecomposable if there is a clopen partition A1,…,An of A and elements g1,…,gn of G such that g1A1,…,gnAn form a partition of B). I will discuss how some properties of the action can be studied via the clopen type semigroup; I will focus in particular on the dynamical comparison property (following Kerr and Ma), and the existence of a dense locally finite group in the topological full group associated to the action. I will also try to outline some consequences for generic properties of minimal actions of a given countable group on the Cantor space, and discuss some open problems.
Information: Please see the seminar webpage.

CMU Logic Seminar
Time: Tuesday, 28 February,  3:30 – 4:30pm Pittsburgh time (21:30 – 22:30 CEST)
Speaker:  Marcin Sabok, McGill University
Title: Perfect matchings in hyperfinite graphings
Abstract: The talk will focus on recent results on measurable perfect matchings in hyperfintie graphings. In particular, we will discuss a result saying that every regular hyperfinite one-ended bipartite graphing admits a measurable perfect matching. We will also see some applications of these results, answering several questions in the field. For instance we will characterize the existence of factor of iid perfect matchings in bipartite Cayley graphs, extending a result of Lyons and Nazarov. We will also answer a question of Bencs, Hruskova and Toth arising in the study of balanced orientations in graphings. Finally, we see how the results imply the measurable circle squaring. This is joint work with Matt Bowen and Gabor Kun.
Information: See the seminar webpage.

Leeds Models and Sets Seminar
Time: Wednesday, 1 March, 13:45-15:00 local time (14:45-16:00 CET)
Speaker: Jiachen Yuan, University of Leeds
Title: How far is almost strong compactness from strong compactness
Abstract: Almost strong compactness of $\kappa$ can be characterized as follows: for every $\delta < \kappa < \lambda$, there is an elementary embedding $j_{\delta,\lambda}: V \rightarrow M$ with critical point $\geq \delta$, so that $j_{\delta,\lambda}“ \lambda \subseteq D \in M$ and $M \vDash |D|< j_{\delta,\lambda}(\kappa)$. Boney and Brooke-Taylor were wondering whether almost strong compactness is essentially the same as strong compactness. Recently, Goldberg showed that if $\kappa$ is of uncountable cofinality and SCH holds from below then these two closely related concepts are the same. In this joint work with Zhixing You, we show that these two can be different in general cases.
Information: Please see the seminar webpage.

Barcelona Set Theory Seminar
Time: Wednesday, 1 March, 16:00-17:30 CET
Speaker: Boriša Kuzeljević
Title: Lower bounds of sets of P-points
Abstract: We will sketch the proof that MA(k) implies that each
collection of Pc-points of size at most k which has a Pc-point as an
RK upper bound also has a Pc-point as an RK lower bound. This is
joint work with Dilip Raghavan and Jonathan Verner.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Vienna Logic Colloquium
Time:
Thursday, 2 March, 15:00 – 15:45 CET
Speaker: Katrin Tent, University of Münster
Title: Simplicity of automorphism groups of homogeneous structures
Abstract: We discuss some general criteria that can be used to show that the automorphism group of a homogeneous structure (such as metric space, right-angled building, graph or hypergraphs) are simple groups or have simple quotients.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

Cross-Alps Logic Seminar
Time: Friday, 3 March 16.00-18.00 CET
Speaker: Dugald Macpherson, University of Leeds
Title: Uniform families of definable sets in finite structures
Abstract: A 1992 theorem of Chatzidakis, van den Dries and Macintyre, stemming ultimately from the Lang-Weil estimates, asserts, roughly, that if ϕ(x,y) is a formula in the language of rings (where x,y are tuples) then the size of the solution set of ϕ(x,a) in any finite field F of size q (where a is a parameter tuple from F) takes one of finitely many dimension-measure pairs as F and a vary: for a finite set E of pairs (μ,d) (μ rational, d integer) dependent on ϕ, any set ϕ(F,a) has size roughly μqd for some (μ,d)∈E.
This led in work of Elwes, Steinhorn and myself to the notion of ‘asymptotic class’ of finite structures (a class satisfying essentially the conclusion of Chatzidakis-van den Dries-Macintyre). As an example, by a theorem of Ryten, any family of finite simple groups of fixed Lie type forms an asymptotic class. There is a corresponding notion for infinite structures of ‘measurable structure’ (e.g. a pseudofinite field, by the Chatzidakis-van den Dries-Macintyre theorem). Any ultraproduct of an asymptotic class is measurable, and in particular has supersimple theory (in the sense of stability theory).
I will discuss a body of work with Sylvy Anscombe, Charles Steinhorn and Daniel Wolf which generalises this, incorporating a richer range of examples with fewer model-theoretic constraints; for example, the corresponding infinite ‘generalised measurable’ structures, for which the definable sets are assigned values in some ordered semiring, need no longer have ‘simple’ theory. I will also discuss a variant in which sizes of definable sets in finite structures are given exactly rather than asymptotically.
Information: The event will stream on the Webex platform. Please write to  luca.mottoros [at] unito.it  for the link to the event.

Toronto Set Theory Seminar
Time: Friday, 3 March, 1.30-3.00 Toronto time (19.30-21.00 CET)
Speaker: Slawomir Solecki, Cornell University
Title: Closed groups generated by generic measure preserving transformations
Abstract: The talk will be about the Polish group of all measure preserving transformations. The behavior of a measure preserving transformation, even a generic one, is highly non-uniform. In contrast to this observation, a different picture of a very uniform behavior of the closed group generated by a generic measure preserving transformation $T$ has emerged. This picture included substantial evidence that pointed to these groups (for a generic $T$) being all topologically isomorphic to a single group, namely, $L^0$—the Polish group of all Lebesgue measurable functions from $[0,1]$ to the circle. In fact, Glasner and Weiss asked if this is the case. I will describe the background touched on above. I will indicate a proof of the following theorem that answers the Glasner–Weiss question in the negative: for a generic measure preserving transformation $T$, the closed group generated by $T$ is {\bf not} topologically isomorphic to $L^0$. The proof rests on an analysis of unitary representations of the non-locally compact group $L^0$