201011
Fridays

Speaker and Talk
Title

June 24
Room 210 
Peter Krautzberger
(Michigan)
Union ultrafilters are fascinating — a survey 
June 17
Room 210 
Dilip Raghavan
(Fields)
Weak squares

201011

PAST SEMINARS

June 10
Room 210 
Paul Larson
Choosing Ideals
We show that, in certain inner models of determinacy, there
is a definable procedure which, given a tall ideal $I$ on $\omega$
containing all finite sets, and a function from $I \setminus
\mathrm{Fin}$ to a countable set, chooses a finite subset of
the range of this function. In the case we are most interested
in, $I$ is generated by a countable collection of pairwise orthogonal
ideals. In this context, $I$ represents a $\mathcal{P}(\omega)/\mathrm{Fin}$name
for an element of a countable set. Our result then says that,
whenever $M[U]$ is a $\mathcal{P}(\omega)/\mathrm{Fin}$extension
of a model $M$ of the type we consider here, if $F$ is a function
in $M[U]$ with domain $X \in M$, and $G$ is a function in $M$
with domain $X$ such that, for all $x \in X$, $F(x) \in G(x)$
and $G(x)$ is countable, then there exists a function $G'$ in
in $M$ with domain $X$ such that, for all $x \in X$, $G'(x)$
is a finite subset of $G(x)$. This gives another proof of a
theorem of Di PriscoTodorcevic that in $M[U]$ there is no function
which selects a single member from each $E_{0}$equivalence
class, where $E_{0}$ is the relation of modfinite agreement
on the Baire space.

June 3
Room 210 
No Seminar

May 27 1:30 to 3pm
Room 210 
Jan van Mill (VU Amsterdam)
Homeomorphism groups of homogeneous compacta need not
be minimal
We present an example of a homogeneous compact space,
the homeomorphism group of which is not minimal. This answers
a question of Stoyanov from about 1984. If time permits, we
will also talk about unique homogeneity and raise some open
problems.

Friday, May 20 
No seminar 
Friday, May 13 from 1:30 to
3pm
Fields Institute, Room 210 
Peng Yinhe (Toronto
and Singapore)
An L space with nonLindelof square
There is an L space with nonLindelof square. Moreover, there
is an L space with some stronger property that its square is
the closure of a countable union of closed discrete subsets. 
May 6
1:30 p.m.
Room 210 
Vladimir Pestov
(Ottawa)
Some settheoretic motives in statistical learning theory
II
We will discuss a few instances where the VapnikChervonenkis
theory of statistical learning has potentially interesting
overlaps with set theory / model theory / extremal combinatorics.
This will be illustrated on speaker's recent results about
PAC learnability over nonatomic measures (a solution of a
problem by Vidyasagar with the help of Martin's Axiom), as
well as learnability over exchangeable data inputs, and a
reputed 25year old open problem concerning the socalled
sample compression schemes.
Slides of talk
http://settheorytalks.files.wordpress.com/2011/05/pestov6may2011.pdf

Apr. 29
1:30 p.m.
Room 210 
NO SEMINAR

Apr. 15
1:30 p.m.
Room 210 
Harvey Friedman
(Ohio State)
Concrete mathematical incompleteness
An unprovable theorem is a theorem about basic mathematical
objects that can only be proved using more than the usual
axioms for mathematics (ZFC = Zermelo Frankel set theory with
the Axiom of Choice)  and that has been proved using standard
extensions of ZFC generally adopted by the mathematical logic
community.
The highlight of the talk is the presentation of unprovable
theorems stated in terms of self embeddings of maximal cliques
in graphs.
We first review some previous examples of unprovable theorems.
15 are unprovable in the weaker sense that any proof demonstrably
requires some use of logical principles transcendental to
the problem statement. 6 is BRT (Boolean Relation Theory).
1. Patterns in finite sequences from a finite alphabet.<br>
2. Pointwise continuous embeddings between countable sets
of reals (or more concretely, rationals).<br> 3. Relations
between f(n_1,...,n_k) and f(n_2,...,n_k+1).<br> 4.
Homeomorphic embeddings between finite trees.<br> 5.
Borel sets in the plane and graphs of one dimensional Borel
functions.<br> 6. Boolean relations between sets of
integers and their images under integer functions.

April 8
1:30 p.m.
Room 210 
Natasha May
(York), Saeed Ghaseemi (York), Amit Gupta (Berkeley)
Research Glimpses 2
On *isomorphisms between the Calkin Algebra onto the tensor
product of two copies of itself; On Conjectures of Rado and
Galvin; and more

April 1
1:30 p.m.
Room 210 
Jim McGarva,
Francisco Kibedi, Christopher Eagle and Dana
Bartosova
Research glimpses 1. (Including topics: Maximal saturated
linear orders, Thintall spaces and PCF structures, and more) 
Mar. 25
1:30 p.m.
Room 210 
J. LopezAbad
(ICMAT, Madrid)
Unconditional sequences in Banach spaces of high density
It is well known that there are separable Banach spaces without
unconditional basic sequences, and that every Banach space
whose density is bigger than an $\omega$Erdös cardinal
contains an unconditional basic sequence. We prove that it
is consistent that every Banach space of density bigger than
$\aleph_\omega$ has an unconditional sequence. Consequently,
it is consistent that every Banach space of such density has
a separable quotient.
The proof relies on a Ramseylike combinatorial property
that $\aleph_\omega$ may have.
This is a joint work with P. Dodos (Athens) and S. Todorcevic
(Toronto).

Mar. 18
1:30 p.m.
Room 210 
J. LopezAbad
(ICMAT, Madrid)
Unconditional sequences in Banach spaces of high density
It is well known that there are separable Banach spaces without
unconditional basic sequences, and that every Banach space
whose density is bigger than an $\omega$Erdös cardinal
contains an unconditional basic sequence. We prove that it
is consistent that every Banach space of density bigger than
$\aleph_\omega$ has an unconditional sequence. Consequently,
it is consistent that every Banach space of such density has
a separable quotient.
The proof relies on a Ramseylike combinatorial property
that $\aleph_\omega$ may have.
This is a joint work with P. Dodos (Athens) and S. Todorcevic
(Toronto).

Mar. 11
1:30 p.m.
Stewart Library 
No Seminar

Mar. 4
1:30 p.m.
Room 210 
Ilijas Farah
(York)
Order property of II_1 factors and its applications II 
Feb. 25
1:30 p.m.
Stewart Library 
Ilijas Farah
(York)
Order property of II_1 factors and its applications

Feb. 18
1:30 p.m.
Room 210 
Jocelyn Bell
(Buffalo)
The Uniform Box Product Problem
An important unsolved problem in topology is the box product
problem, which asks whether the product of compact spaces
with the box topology is normal. Applying uniformities, we
introduce a new topology on products which sits between the
box and Tychonov products called the uniform box product.
This new product is an extension of the sup metric to products
of compact spaces. We will show, in ZFC, that the uniform
box product of a certain nonmetrizable compact space is normal.

Feb. 11
1:30 p.m.
Room 210 
Paul Szeptycki (York)
A Lindelof T_1 space that is not a Dspace

Feb. 4
1:30 p.m.
Room 210 
Stevo Todorcevic (Toronto)
A higherdimensional theory of gaps in P(N)/Fin, part III 
Jan. 28
1:30 p.m.
Room 210 
Stevo Todorcevic (Toronto)
A higherdimensional theory of gaps in P(N)/Fin, part II

Jan. 21
1:30 p.m.
Room 210 
Stevo Todorcevic (Toronto)
A higherdimensional theory of gaps in P(N)/Fin

Jan. 14
1:30 p.m.
Room 210 
Jakub Jasinski (Toronto)
Boron Tree Structures 
Jan. 7
1:30 p.m.
Room 210 
Jakub Jasinski (Toronto)
Finite subsets of finite dimensional Euclidean spaces

Dec. 17
1:30 p.m.
Room 210 
**NO SEMINAR** 
Dec. 10
1:30 p.m.
Room 210 
Max Burke (PEI)
Liftings and densities for derived algebras

Dec. 3
1:30 p.m.
Room 210 
Samuel Coskey
(Fyorks Universitute)
Borel equivalence relations and models of arithmetic 
Nov. 26
1:30 p.m.
Room 210 
NO
SEMINAR 
Nov. 19
1:30 p.m.
Room 210 
Vladimir Pestov
(University of Ottawa)
Some settheoretic motives in statistical learning theory
A set theorist will find interesting opportunities by turning
to the VapnikChervonenkis theory of statistical learning.
To argue this point, we will discuss the basic concepts and
results of the theory of probably approximately correct (PAC)
learnability, and then proceed to some recent results by the
speaker. Those include a solution of a problem by Vidyasagar
about PAC learnability over nonatomic measures which use
Martin's Axiom and a combinatorial parameter defined for Boolean
algebras. We will also discuss some other results and open
problems.

Nov. 12
1:30 p.m.
Room 210 
Juris Steprans
(York)
Reflecting nonmeagreness in the ErdosKakutani group (joint
work with Marton Elekes)

Nov. 5
1:30 p.m.
Room 210 
Todor Tsankov
(Paris VI)
Applications of Roelcke precompactness to representation
theory
I will discuss the notion of Roelcke precompactness and how
it can be applied to the study of unitary representations.
I plan to give a fairly complete proof of the classification
theorem for the representations of automorphism groups of
omegacategorical structures.

Oct. 22
1:30 p.m.
Room 210 
Julien Melleray
(Lyon)
Polish topometric groups

Oct. 29
1:30 p.m.
Room 210 
Lionel Nguyen
Van Thé (Université AixMarseille 3, Paul
Cézanne)
Partition properties of the dense local order
(joint with Claude Laflamme and Norbert Sauer, University of
Calgary)
In 1984, Lachlan classified the countable ultrahomogeneous
tournaments (ie the countable directed graphs where every
pair or points supports an arc, and where every isomorphism
between finite subgraphs extends to an automorphism of the
whole structure), and showed that there are only three such
objects: the rationals, the countable random tournament, and
the socalled dense local order. The purpose of this talk
is to present the Ramsey properties of this latter object.

Oct. 15 
No seminar on Friday, October 15
due to:Workshop
on the Concentration Phenomenon, Transformation Groups and
Ramsey Theory
October 1215
Fields Institute

Oct. 8
1:30 p.m.
Rm 210 
Peter Burton (UofT)
CH implies the existence of stationary locally countable families;
hence CH implies productively Lindelof spaces are powerfully
Lindelof.
(And, if time remains)
Frank Tall (UofT)
More applications of PFA(S)[S]

Sep 24
1:30 p.m.
Fields Rm 210 
Peter Burton, Kevin Duanmu, Frank Tall (U of T)
Lindelof products
A problem in Przymusinski's Handbook survey on normality
of products asks whether, if X x Y is Lindelof for every Lindelof
Y, are all countable powers of X Lindelof. We show that the
Continuum Hypothesis implies a positive answer.

Sep 17
1:30 p.m.
Fields Rm 210 
Peter Burton, Kevin Duanmu, Frank Tall (U of T)
Lindelof products
A problem in Przymusinski's Handbook survey on normality
of products asks whether, if X x Y is Lindelof for every Lindelof
Y, are all countable powers of X Lindelof. We show that the
Continuum Hypothesis implies a positive answer.

Sep 10
1:30 p.m.
Fields
Rm 210 
Franklin Tall, University of Toronto
More applications of PFA(S)[S]

Friday,
Sept. 3 
No Seminar 
Friday,
August 27 
Asger Törnquist
( KCRG Wien)
Conjugacy, orbit equivalence and von Neumann equivalence
are analytic.
For a countably infinite discrete group G, there are three
equivalence relations of major interest for its measure preserving
ergodic actions: Conjugacy, orbit equivalence and von Neumann
equivalence. These equivalence relations are prima facie analytic.
Can they be Borel?
For G amenable, only conjugacy is of interest. In the special
case G=Z the question goes back to Halmos, but was only recently
solved by Forman, Rudolph and Weiss, who showed that conjugacy
is complete analytic (as a
set.)
In this talk I will show that for a class of nonamenable groups,
including all free groups, that all three of the above equivalence
relations are analytic and not Borel.
Part of this work is joint with Inessa Epstein.

Friday,
August 20 
Ilijas Farah (York)
A very short introduction to Woodin's Pmax forcing

Friday,
August 13 
Paul Larson (Miami University
of Ohio)
Fragments of Martin's Maximum in the Pmax extension

Friday,
August 6 
Franklin Tall
PFA(S)[S] and applications cont.
We develop machinery for applying the method of forcing
with a coherent Souslin tree S over models of PFA restricted
to posets that preserve S. 
Friday,
July 30 
Franklin Tall
PFA(S)[S] and applications
We develop machinery for applying the method of forcing
with a coherent Souslin tree S over models of PFA restricted
to posets that preserve S. 
Friday,
July 23

Dilip Raghavan (Fields)
A Hausdorff real without dominating reals

Friday,
July 16 
No Seminar

Friday,
July 9

Sam Coskey (CUNY)
Classification and equivalence relations


