Winter 2024

Upcoming talks:

March 12: Postponed

March 5: Break

February 27: Clement Yung (University of Toronto)

Title: MAD Families of Gowers' Infinite Block Sequences (Continued)

Abstract: This is a continuation of the previous talk by the same speaker. We shall finish the proof that we can obtain a valuation for the ideal of small subsets of FIN_k. Original abstract: Call a subset of FIN_k small if it does not contain a copy of [P] for some infinite block sequence P. Gowers' FIN_k theorem asserts that the set of small subsets of FIN_k forms an ideal, so it is sensible to consider almost disjoint families of FIN_k with respect to the ideal of small subsets of FIN_k. In this talk, I'll provide a (mostly visual) proof that the smallest possible cardinality of an infinite mad family of FIN_k is uncountable.

February 20: Break 

February 13: Clement Yung (University of Toronto)

Title: MAD Families of Gowers' Infinite Block Sequences

Abstract: Call a subset of FIN_k small if it does not contain a copy of [P] for some infinite block sequence P. Gowers' FIN_k theorem asserts that the set of small subsets of FIN_k forms an ideal, so it is sensible to consider almost disjoint families of FIN_k with respect to the ideal of small subsets of FIN_k. In this talk, I'll provide a (mostly visual) proof that the smallest possible cardinality of an infinite mad family of FIN_k is uncountable.

Past talks:

February 6: Khulod Almontashery (York University)

Title: Proximal and Semi-proximal Spaces

Abstract: Jocelyn Bell introduced the notion of proximal spaces using uniformities to address problems related to uniform box products. A proximal space is a topological space X for which there exists a compatible uniformity such that Player I has a winning strategy in a specific two-player game of infinite length. I will give an exploratory introduction about the classes of spaces related to this game and share some recent joint work with Paul Szeptycki about the relationship of these spaces to normal topological spaces.

January 30: Lucas O'Brien (University of Toronto)

Title: The Normality of Products under Perfect Preimage

Abstract: This talk will provide a discussion of the normality of products with a compact factor, providing a solution to an open problem attributed to Kunen.

January 23: Luciano Salvetti (University of Toronto)

Title: Classifying generic extensions

Abstract: Fix a countable transitive model M of ZFC and fix your favourite forcing poset in M. Say that two M-generic filters are equivalent if they produce the same generic extensions. In this talk we will discuss basic properties of this Borel equivalence relation. I will also expose open problems related to this topic which I find interesting. The content of the talk is mainly based on a paper by Iian B. Smythe.