SCIENTIFIC PROGRAMS AND ACTIVITIES

September 19, 2014

Set Theory Seminar Series at the Fields Institute
Friday, 1:30 p.m.

Organizers:
Ilijas Farah,
York University, Juris Steprans, York University.

For a complete listing of seminars and abstracts: http://www.math.yorku.ca/~ifarah/seminar.html

2007
Speaker and Talk Title
Friday
June 22
Max Burke (Prince Edward Island)
Title: TBA
Friday
June 15
Frank Tall (University of Toronto)
On the metrizability of hereditarily normal manifolds of dimension > 1, (continued)
Friday
June 8
Franklin Tall (University of Toronto)
On the metrizability of hereditarily normal manifolds of dimension > 1.
We show that a conjunction of four axioms, three of which are consequences of PFA and one of which is a consequence of V = L, implies such manifolds are metrizable. The consistency of such a result is a long-outstanding conjecture of Peter Nyikos. Two of the axioms are known to follow from PFA(S)[S]; I conjecture that the other two also follow.
Friday
June 1
Paul Szeptycki (York University)
Normality in products with a countable factor.
Friday
May 25
Cancelled
Friday
May 18
Philip Kremer (Department of Philosophy, University of Toronto)
Dynamic Topological Logic
Friday
May 11
Arthur Fischer (University of Toronto)
'Balogh's Sigma' in models of the form PFA(S)[S] (continued)
Friday
May 4
Arthur Fischer (University of Toronto)
'Balogh's Sigma' in models of the form PFA(S)[S] (continued)
Friday
April 27
Arthur Fischer (University of Toronto)
Balogh's Sigma' in models of the form PFA(S)[S]
Continuing the study of topological consequences of forcing with the coherent Souslin tree S in models of PFA(S), we will demonstrate that the following PFA result also holds: Every locally countable subspace Z of size aleph-1 in a compact sequential space X is sigma-closed discrete in some open neighbourhood of Z in X which "locally witnesses" the local countability of Z in X.
Friday
April 20
Paul Larson (Miami University, Ohio)
The stationary set splitting game.
Friday
April 13
Matthias Neufang
(title is to be announced)
Friday
April 6
no talk
Friday,
March 30
Wieslaw Kubis, Kielce, Poland
Fraisse sequences and their limits - a category-theoretic approach
Given a category, we define the notion of a Fraisse sequence: an inductive sequence which shares the properties of a typical chain of model-theoretic structures producing the Fraisse-Jonsson limit structure. We give a criterion for the existence of a Fraisse sequence of a given length and we shall present some sufficient conditions for its homogeneity, universality and uniqueness. For instance: a fixed category may have, up to isomorphism, at most one countable Fraisse sequence. We give an example of a certain category of countable trees with many non-isomorphic Fraisse sequences of length aleph one.
Finally, we shall present some applications for constructing universal objects in certain natural categories of compact spaces, Banach spaces and linearly ordered sets.
Friday,
March 23
Slawomir Solecki
Polish Groups as Isometry Groups.
Friday,
16 March
1:30PM
Stevo Todorcevic, University of Toronto
Chain Conditions in Topology, III.
Friday,
March 9
Stevo Todorcevic, University of Toronto
Chain Conditions in Topology, III
Friday,
23 February
3:30PM,
Andrew Toms, York University
Elliott's program and partially ordered Abelian groups.
We give a (hopefully) not-too-technical introduction to Elliott's program to classify separable amenable C*-algebras via K-theoretic invariants. We will stress the role of partially ordered Abelian groups, and discuss how the decomposition of such groups into inductive limits of tractable building blocks gives attractive range results for K-theoretic invariants. Some time will also be spent on the question of "how many" such groups may arise as the K-groups of simple C*-algebras. Finally, if time permits, we will point out some recent results in C*-algebra theory which have a set theoretic flavour.
February 16 (cancelled)
 
Friday
February 9,
1:30 pm
Victoria Lubitch
Note on quasi-Rosenthal compactum.
Let X be a polish space. A compact subset K of R^X is called quasi-Rosenthal if the accumulation points of K are Baire-1 functions. S.A Argyros, P. Dodos, V.Kanellopoulos asked whether every quasi-Rosenthal compactum is Frechet. I will present a counter-example.
February 2,
1:30 pm
Wieslaw Kubis, Kielce, Poland
Compact spaces generated by retractions
I will discuss some results on the class of compact spaces obtained by closing the class of metric compact by inverse limits of retractions.

Friday,
January 26
1:30 pm


Luis Pereira
Cardinal estimates using a topological approach
We will prove that Shelah's application of his estimates of the Galvin-Hajnal norm to cardinal arithmetic can be obtained via Shelah's PCF topology alone.
January 19
Vladimir Pestov, University of Ottawa
Subgroups of metric ultraproducts of unitary and of symmetric groups: hyperlinear and sofic groups
Relatively recently, two new classes of groups have been isolated: hyperlinear groups and sofic groups. They come from different corners of mathematics (operator algebras and symbolic dynamics, respectively), and were introduced independently from each other, but are closely related nevertheless. Hyperlinear groups are motivated by Connes' Embedding Conjecture about von Neumann factors of type II_1 and go back to Connes' work, while sofic groups, introduced by Gromov, are motivated by Gollschalk surjunctivity conjecture (can a shift A^G contain a proper isomorphic copy of itself, where A is a finite discrete space and G is a group?). Groups from both classes can be characterized as subgroups of metric ultraproducts of families of certain metric groups (formed in the same way as ultraproducts of Banach spaces): unitary groups of finite rank lead to hyperlinear groups, symmetric groups of finite rank - to sofic groups. We will survey results by Connes, Gromov, Benjy Weiss, Ozawa, Elek and Szabo, Radulescu, and Gordon, and also discuss open questions which are for the time being perhaps more numerous than the results.
The slides from Vladimir Pestov's seminar talk are now available. You can either download them at
http://aix1.uottawa.ca/~vpest283/textes/07-01b-4.pdf
or you can find them at the seminar web page:
http://www.atkinson.yorku.ca/~szeptycki/seminar/seminar06.html
January 12
Bernhard Koenig, University of Toronto
Coherent trees (continued).
January 5
Bernhard Koenig, University of Toronto
Coherent trees.
2006
 
December 8
Frank Tall, University of Toronto
Forcing with coherent Souslin trees (Continued)
We shall continue developing the technology for forcing with coherent Souslin trees.
December 1
Frank Tall, University of Toronto
Forcing with coherent Souslin trees
We shall start developing the technology for forcing with coherent Souslin trees. This lecture will be independent of previous ones on PFA(S)[S].
November 24,
1:30 pm
Bernhard Koenig, University of Toronto
Forcing Axioms and their fragments (continued)
November 17, 1:30PM
Frank Tall, University of Toronto
Applications of PFA(S)[S] (continued)
We continue setting up the machinery we started last time, for applications proving collectionwise Hausdorffness.
November 10,
1:30 pm
Bernhard Koenig, University of Toronto
Forcing Axioms and their fragments
We talk about fragments of the forcing axioms PFA or MM, e.g. PFA for posets not adding reals or MM for forcings with the covering property. The theorems we present give a good overview of the strengths of these fragments. Many results are of the following form: start with a model of MM and add an object of size aleph_2 generically; this might destroy the full forcing axiom but very often the extension is mild enough to preserve a fragment of the forcing axiom.
November 3,
1:30 pm
Asger Tornquist
Non-classification Theorems for conjugacy and orbit equivalence of measure preserving ergodic actions, Part IV.
October 27,
1:30 pm
Asger Tornquist
Non-classification Theorems for conjugacy and orbit equivalence of measure preserving ergodic actions, Part III.
October 20,
1:30 pm
Frank Tall, University of Toronto.
Further Topological Applications of PFA(S)[S]
October 13,
1:30 pm
Frank Tall
Locally compact spaces, paracompactness, and large cardinals
By considering localized reflection principles and non-reflecting stationary sets, we distinguish the consistency strength of two propositions concerning the paracompactness of locally compact normal spaces.
October 6,
1:30 pm
Asger Tornquist
Non-classification theorems for conjugacy and orbit equivalence of measure preserving ergodic actions (PART II)
We give a new proof and a strengthening of a Theorem of Foreman and Weiss, stating that the measure preserving a.e. free ergodic actions of a countably infinite group cannot be classified up to conjugacy by countable structures. Using this strengthened version, we show that the measure preserving ergodic a.e. free actions of a countable group with the relative property (T) over an infinite normal subgroup cannot be classified up to orbit equivalence by countable structures.
Friday,
September 29,
1:30 pm
Asger Tornquist
Non-classification theorems for conjugacy and orbit equivalence of measure preserving ergodic actions.
We give a new proof and a strengthening of a Theorem of Foreman and Weiss, stating that the measure preserving a.e. free ergodic actions of a countably infinite group cannot be classified up to conjugacy by countable structures. Using this strengthened version, we show that the measure preserving ergodic a.e. free actions of a countable group with the relative property (T) over an infinite normal subgroup cannot be classified up to orbit equivalence by countable structures.
September 22,
1:30 pm
Frank Tall
PFA(S)[S] and Small Dowker Spaces
There have been only a few consistency results excluding particular kinds of "small" examples of normal spaces with product with the unit interval not normal, but a plethora of consistency results providing such examples. We restore the balance, using a model of Todorcevic.
September 8
Discussion of Shelah's paper The combinatorics of reasonable ultrafilters
(this is Sh:830 2004-07-28 downloadable from the Shelah archive http://shelah.logic.at/)
July 28
we will continue to read Shelah's paper The combinatorics of reasonable ultrafilters.
(this is Sh:830 2004-07-28 downloadable from the Shelah archive http://shelah.logic.at/)
July 21
Peter Komjath
Uncountable chromatic triple systems
July 14
Discussion of Shelah's paper The combinatorics of reasonable ultrafilters
(this is Sh:830 2004-07-28 downloadable from the Shelah archive http://shelah.logic.at/)
July 07
TBA


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