2008/09
Fridays

Speaker and Talk
Title

*Monday June 1*
Fields Institute
Room 210 
10:3012:00 Speaker KP Hart (Miami University, Ohio
and Delft, Netherlands)
Title: TBA
1:303:00 Speaker Marion Scheepers (Boise State)
Title: TBA
3:305:00 Speaker: Paul Larson (Miami University,
Ohio)
Title: Universally measurable sets in generic extensions.

Wednesday,
May 27*
1:303:00 in BA6183 on 6th fl. Bahen Centre 
OF NOTE
Speaker: Gary Gruenhage (Auburn)
Title: SLIM DENSE SETS IN PRODUCTS 
*Thursday
May 28*
1:303:00 in Bahen Centre 6183 
OF NOTE
Speaker: Justin Moore (Cornell)
Title: Fast growth of the Folner function for Thompson's group
F. 
May 22, 2009
1:303:00 
Beatriz ZamoraAviles (York University)
Analytic Pideals on $B(H)^+_{\leq
1}$ 
May 15, 2009
1:303:00 
Tamas Matrai (University of
Toronto)
Infinite dimensional perfect set theorems
We obtain infinite dimensional analogues of some classical perfect
set theorems, and we indicate how these result can be applied
to the study of analytic ideals. 
May 8, 2009 
No talk scheduled 

Slides of
Talk
Simon Thomas (Rutgers University)
Some Consequences of Martin's Conjecture
Abstract: In this talk, I will explore some of the consequences
of Martin's Conjecture on degree invariant Borel maps. These
include the strongest conceivable ergodicity result for the
Turing equivalence relation, as well as the statement that the
complexity of a universal countable Borel equivalence relation
always concentrates on a null set. 
April 24, 2009
1:303:00 
lijas Farah (York University)
Nonseparable UHF algebras
Uniformly HyperFinite (UHF) algebras are those C* algebras in
which every finite subset is `near' a finitedimensional full
matrix subalgebra. This can be formalized in three different
ways, all three being equivalent in the separable case. Separable
UHF algebras were classified in the 1960s by Glimm and Dixmier.
Dixmier asked whether three definitions are equivalent in the
nonseparable case. I will give a complete answer to this question
as well as some remarks on extending the GlimmDixmier theorem
to the nonseparable case.
This is a joint work with Takeshi Katsura. 
April 17, 2009
1:303:00

Frank Tall (University of Toronto)
Lindelof spaces and selection principles, II.
We continue our investigation of Lindelof spaces and selection
principles, focusing on the relationships among productive
Lindelofness and the Menger and Hurewicz properties.

March 27/09
1:303:00 
Jordi Lopez Abad (Universite DenisDiderot Paris7)
Generic constructions of Banach spaces.
The aim of this talk is to present a forcing construction
"à la Cohen" of generic Banach spaces. These
spaces are Gurarij spaces, and in the case of the nonseparable
context, they can be nonisomorphic. These constructions can
also be used to distinguish the existence of different kind
of uncountable biorthogonallike sequences.
This is a joint work with S. Todorcevic.

March 20/09
1:303:00 
Arnie Miller (University of Wisconsin,
Madison)
The hierarchy of $\omega_1$Borel sets
The family $\omega_1$Borel sets is the smallest family of subsets
of the real line which contains the family of open sets and
is closed under complementation and $\omega_1$ unions. We show:
Theorem 1. MA + not CH implies this hierarchy has length $\omega_2$.
Theorem 2. In the Cohen real model it has length either $\omega_1+1$
or $omega_1+2.

March 20/09
3:15  4:45 
Natasha Dobrinen, (University of Denver)
Tukey degrees of ultrafilters
Let $U$ and $V$ be ultrafilters on $\omega$. We say that $V$
is Tukey reducible to $U$ ($V\le_T U$) if there is a "Tukey
map" $g: V\rightarrow U$, meaning that $g$ maps unbounded
subsets of $V$ to unbounded subsets of $U$. Equivalently, there
is a "cofinal" map $f: U\rightarrow V$ which maps
cofinal subsets of $U$ to cofinal subsets of $V$. Tukey reducibility
is a generalization of RudinKeisler reducibility.
In general, $V\le_{RK} U$ implies $V\le_T U$ but not vice versa.
However, it is still unknown if this is the case for ppoints.
We present some results on the structure of the Tukey degrees
of ultrafilters on $\omega$, concentrating on ppoints and ultrafilters
with similar properties, along with many
questions.
This is joint work with Stevo Todorcevic. 
March 13
1:303:00 
Alexander Pyshchev (Nipissing University)
On nonstandard hulllike spaces.
We investigate topological spaces obtained as quotients of
internal sets in a nonstandard universe.

March 13
3:15  4:45 
Carlos DiPrisco, (IVIC, Venezuela)
Chromatic numbers of analytic shift graphs 
February 27

Christopher Miller (Ohio State University)
Tameness in expansions of the real field
What should it mean for a firstorder expansion of the
field of real numbers to be tame, or well behaved? In recent
years, much attention has been paid by model theorists and
realanalytic geometers
to the ominimal setting: expansions of the real field in
which every definable set has finitely many connected components.
But there are expansions of the real field that are tame in
some welldefined sense, yet define sets with infinitely many
connected components. Moreover, there are different kinds
of tameness that can arise. The analysis of these structures
tends to require a mixture of modeltheoretic,
analyticgeometric and descriptive settheoretic techniques.
Underlying all this is an idea that firstorder definability,
in combination with the field structure, can be used as a
tool for determining how
complicated given sets of real numbers are, in particular,
this gives us a new way to think about projective sets. This
will be a primarily expository survey talk, intended to be
accessible to anyone with a background in basic logic.

February 20
1:303:00 
Frank Tall (University
of Toronto)
Selection principles and Lindelof
spaces which are indestructible, productive, or D. 
February 13
2:00  3:30

Dilip Raghavan (University
of Toronto)
Suslin Lattices (Continued) 
February 6, 2009
2:00  3:30

Dilip Raghavan (University of Toronto)
Suslin Lattices 
January 23/09
1:303:00 
Leandro Aurichi (University of Sao Paolo)
TBA 
January 16/09
1:303:00 
Asger Tornquist (University
of Vienna)
Borel reducibility and von Neumann equivalence 
January 9/09
1:303:00 
Lionel Nguyen Van Thé
(University of Calgary)
Problems and results around metric oscillation stability.
In 1994, Odell et Schlumprecht built a uniformly continuous
map from the unit sphere of the Hilbert space into
the unit interval and which does not stabilize on
any isometric copy of the sphere. This antiRamsey result
allowed to show that the Hilbert space has a property known
as 'distortion'. The purpose of this talk is to consider
similar problems when the Hilbert space is replaced
by the socalled Urysohn metric space. 
December 19,
1:303:00

Tamas Matrai (University of Toronto)
Sigmaideals of compact sets in the Tukey ordering, continued

December 12
1:303:00 
Tamas Matrai (University of
Toronto)
Sigmaideals of compact sets in the Tukey ordering
We introduce a construction scheme of G_delta sigmaideals of
compact sets and we try to find the place of the ideals obtained
in the Tukey ordering. 
December 5
1:303:00 
Matthew Foreman (University
of California, Irvine)
Rational Invariant Measures
Global questions about classifications of ergodic measure preserving
transformations are usually studied by adopting one or another
universal model for the measure preserving transformations.
In this lecture I describe a new universal model investigated
in joint work with B. Weiss. The underlying space of this model
is $\Sigma^Z$, where $\Sigma$ is a countable set. The new part
is that the invariant measures are required to give rational
values to each cylindar set. 
November 28
1:303:00 
Leandro Aurichi (University of Sao Palo, Brazil)
Dspaces and games
Some games related to Dspaces, Rothberger and Menger spaces

November 21
1:303:00 
(TALK HAS BEEN CANCELLED this week)
Dilip Raghavan, University of Toronto
The Pideal Dichotomy and Lattices

November 14
1:303:00 
Bernhard Koenig (University of Toronto)
Variations of Axiom (continued)
It is known that Fleissner's Axiom R is basically a variation
of the stationary reflection principle. We investigate the
exact status of Axiom R within the realm of stationary reflection
principles by presenting some implications but also independence
results.

November 7
1:303:00 
Bernhard Koenig (University
of Toronto)
Variations of Axiom
It is known that Fleissner's Axiom R is basically a variation
of the stationary reflection principle. We investigate the exact
status of Axiom R within the realm of stationary reflection
principles by presenting some implications but also independence
results. 
October 31
1:303:00 
Carlos Azarel (University of Toronto)
Well quasiordering Aronszjan lines II
We will prove that under PFA the class of Aronszjan lines is
well quasiordered. 
October 24,
1:303:00 
Carlos Azarel (University of Toronto)
Well quasiordering Aronszjan lines.
We will prove that under PFA the class of Aronszjan lines
is well quasiordered.

October 17,
1:303:00
**Room change
Stewart Library** 
Stevo Todorcevic (University of Toronto
and CNRS Paris)
Forcing with a coherent Souslin tree 
October 10
1:303:00pm

Leandro Aurichi (University of Sao Paolo, Brazil)
The Rothberger and Menger properties
We show some applications of these properties, including
some related to preservation by forcing.

September 19
1:303:00pm

Tamas Matrai (University of Toronto)
Hurewicz testing 
September 12,
1:303:00 
Tamas Matrai (University of Toronto)
Introduction
I would like to present three topics I plan to work on
during my stay in Toronto. These are:
1) Tukey reducibility of ideals and $\sigma$ideals
2) Borel reducibility among $\ell^{p}$like equivalence relations
3) Hurewicz testing

September 5
1:303:00 
Leandro Aurichi (University of Sao Paolo, Brazil)
Trees with fine wedge and coarse wedge topologies.
We present a technique for constructing some examples
of spaces which answer some questions on discretely generated
properties and spaces.

August 29
1:303:00pm 
Asger Tornquist (University
of Toronto)
Essentially countable equivalence relations
A Borel equivalence relation is essentially countable if it
is Borel reducible to a Borel equivalence relation with countable
classes. We will give a new and simpler proof of a Theorem of
Greg Hjorth, which states that there is more essentially countable
Borel equivalence relations than there are Borel equivalence
relations with countable classes. 
August 22
1:303:00pm 
Dilip Raghavan (University of Toronto)
Proof of a conjecture of Brendle

July 11, 2008
room 210 
Dilip Raghavan (University of Toronto)
A Van Douwen MAD family in ZFC. 