The Toronto Set Theory Seminar is normally held on Fridays, from 1:30 to 3pm, in room 210 of the Fields Institute. For listing of talks from years earlier than 2006, see this page.

## Dimitris Vlitas: Canonical equivalence relations on the topological Ramsey space FIN_k

Place: Fields Institute (Room 210)

Date: February 5, 2016 (13:30-15:00)

Speaker: Dimitris Vlitas

Title: Canonical equivalence relations on the topological Ramsey space $FIN_k$

Abstract: As an application of a more general theory recently developed, we give a complete list of all equivalence relations on barriers of the topological Ramsey space $FIN_k$, for all $k$.

## Franklin Tall: Definable Versions of Hurewicz’s Conjecture that Menger Spaces are Sigma-compact

Place: Fields Institute (Room 210)

Date: January 29 , 2016 (13:30-15:00)

Speaker: Franklin Tall

Title: Definable Versions of Hurewicz’s Conjecture that Menger Spaces are Sigma-compact

Abstract: Hurewicz’s conjecture that Menger spaces are sigma-compact is false; it is true for analytic subspaces of Polish spaces and undecidable for other definable subspaces of Polish spaces. For non-metrizable spaces, analytic Menger spaces are sigma-compact, but projections of co-analytic spaces need not be. The co-analytic case may be undecidable, but is not yet settled. We have partial results. Our methods are a mix of non-metric descriptive set theory and Arhangel’skii’s work on generalized metric spaces.

## Diana Ojeda: Topological partition relations for countable ordinals

Place: Fields Institute (Room 210)

Date: January 22 , 2016 (13:30-15:00)

Speaker: Diana Ojeda

Title: Topological partition relations for countable ordinals

Abstract:

The subject of topological partition relations provides answers to questions
of the following form: Given a topological space X and a subspace Y, is it
possible to reduce any given coloring of the pairs of elements of X to a simpler
coloring, by passing to a subspace homeomorphic to Y?

I will first present a survey of topological partition relations for countable
ordinals with the order topology. In many instances it is useful to represent
countable ordinals using families of finite sets. I will describe how to obtain
such representations; and will present results from a joint project with William
Weiss, where we obtain topological partition relations for ordinals below $\omega^2$ with the order topology.

## Dilip Raghavan: Some results in the partition calculus

Place: Fields Institute (Room 210)

Date: January 8th, 2016 (13:30-15:00)

Speaker: Dilip Raghavan

Title: Some results in the partition calculus

Abstract:  I will report on my recent joint work with Stevo Todorcevic on partition relations. One focus will be on getting the consistency of a positive partition relation at the bounding number from large cardinals.

## Ashutosh Kumar: Entire functions with small orbits

Place: Fields Institute (Room 210)

Date: December 11th, 2015 (13:30-15:00)

Speaker: Ashutosh Kumar

Title: Entire functions with small orbits

Abstract: Erdos proved that the existence of an uncountable family of entire functions that take countably many values at each complex number is equivalent to CH. He asked what happens if we replace uncountable by continuum and countable by less than continuum? We show that in this case the answer is independent of ZFC plus not CH. Joint work with Shelah.

## Haosui Duanmu: Nonstandard Analysis and its applications to Markov Chains

Place: Fields Institute (Room 210)

Date: December 4th, 2015 (13:30-15:00)

Speaker: Haosui Duanmu

Title: Nonstandard Analysis and its applications to Markov Chains

Abstract: I will give a short introduction of Nonstandard Analysis, Nonstandard Probability Theory as well as Markov Chain Convergence Theorem. I will give an example to show how to represent Lebesgue measure on [0,1] using Hyperfinite probability measure. Then I will introduce the concept of Hyperfinite Markov chain. For every standard Markov Chain, I will show how to construct a corresponding Hyperfintie Markov Chain. Thus the convergence of the Hyperfinite Markov Chain would imply the convergence of the original Markov Chain.

## Jordi Lopez-Abad: Approximate Ramsey property of matrices and f.d. normed spaces

Place: Fields Institute (Room 210)

Date: November 20th , 2015 (13:00-14:00)

Title: Approximate Ramsey property of matrices and f.d. normed spaces

Abstract: We present the approximate Ramsey property  of  the finite dimensional normed spaces. This is a particular case of a result concerning “metric Ramsey degrees” of matrices. This is a joint work with D. Bartosova and B. Mbombo (U. Sao Paulo)

## Julien Melleray: The simplex of invariant measures of a minimal homeomorphism

Place: Fields Institute (Room 210)

Date: November 20th, 2015 (14:00-15:00)

Speaker: Julien Melleray

Title: The simplex of invariant measures of a minimal homeomorphism

Abstract:  (joint work with Tomás Ibarlucia) We give a characterization
of all simplices of probability measures on a Cantor space X which may
be realized as the simplex of all invariant probability measures for
some minimal homeomorphism g of X. This extends a result of Akin for the
case when K is a singleton, and an unpublished result of Dahl when K is
finite-dimensional. All relevant notions of topological dynamics will be
recalled.

## Chris Eagle: Definability in infinitary [0, 1]-valued logic

Place: Fields Institute (Room 210)

Date: November 13th, 2015 (13:30-15:00)

Speaker: Chris Eagle

Title: Definability in infinitary [0, 1]-valued logic

Abstract: In recent years there have been several proposals for the
“right” analogue of the infinitary logic $L_{\omega_1, \omega}$ for metric
structures.  I will present the three most recent candidates, and discuss
issues around definablity in each of those logics.  The main result is
that in the most expressive of these logics, a continuous [0, 1]-valued
function on a complete separable metric structure is definable if and only
if it is automorphism invariant.

## Yinhe Peng: Higher finite powers of L spaces and higher dimensions of combinatorial properties

Place: Fields Institute (Room 210)

Date: November 6th, 2015 (13:30-15:00)

Speaker: Yinhe Peng

Title: Higher finite powers of L spaces and higher dimensions of combinatorial properties

Abstract: We will see examples of L spaces whose square (or even some higher power) is still an L space (in a joint paper with Liuzhen). We will then see the combinatorial properties behind this and their dimensions.