On locally countable Borel trees, graphs, equivalence relations, and other structures

Speaker(s)

Ronnie Chen

Affiliation

University of Warsaw

Language of the talk

English

Date

Oct. 28, 2026, 4:15 p.m.

Room

room 4050

Seminar

Topology and Set Theory Seminar

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This talk concerns locally countable Borel combinatorial structures, such as graphs, trees, group actions, etc., on Polish spaces (or standard Borel spaces). There is a rich framework, developed over the past four decades by many authors, that gives a detailed global classification of all such structures, with connections to countable model theory and dynamical systems. We will introduce and survey some aspects of this global theory. We will then focus on the particular class of locally countable Borel trees, and describe some recent results that apply large-scale geometric ideas to show that a "tree-like" Borel graph may be turned into a tree in a "uniformly definable" Borel way. The talk will be based on parts of joint works with Rishi Banerjee, Alexander Kechris, Antoine Poulin, Ran Tao, Anush Tserunyan, and Robin Tucker-Drob.

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