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 longoutstanding 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 aleph1 in a compact sequential
space X is sigmaclosed 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 categorytheoretic
approach
Given a category, we define the notion of a Fraisse sequence:
an inductive sequence which shares the properties of a typical
chain of modeltheoretic structures producing the FraisseJonsson
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 nonisomorphic
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) nottootechnical introduction to
Elliott's program to classify separable amenable C*algebras
via Ktheoretic 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 Ktheoretic invariants. Some
time will also be spent on the question of "how many"
such groups may arise as the Kgroups 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 quasiRosenthal compactum.
Let X be a polish space. A compact subset K of R^X is called
quasiRosenthal if the accumulation points of K are Baire1
functions. S.A Argyros, P. Dodos, V.Kanellopoulos asked whether
every quasiRosenthal compactum is Frechet. I will present a
counterexample. 
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 GalvinHajnal 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/0701b4.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
Nonclassification Theorems for conjugacy and orbit equivalence
of measure preserving ergodic actions, Part IV. 
October 27,
1:30 pm

Asger Tornquist
Nonclassification 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 nonreflecting
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
Nonclassification 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
Nonclassification 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 20040728 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 20040728 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 20040728 downloadable from the Shelah archive
http://shelah.logic.at/) 
July 07

TBA 