Borel Equivalence Relations
This course will be an introduction to the theory of Borel equivalence relations, a very active area of descriptive set theory which provides techniques for studying the relative complexity of classification problems in mathematics such as: Is the classification problem for finitely generated groups strictly easier than the classification problem for arbitrary countable groups? Is the classification problem for torsion-free abelian groups of rank 1 strictly easier than the classification problem for torsion-free abelian groups of rank 2? The topics to be covered will include applications of ergodic theory to Borel equivalence relations, as well as some recent applications of Borel determinacy. No prior knowledge of ergodic theory or determinacy will be assumed.
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Familiarity with the basic theory of complete separable metric spaces and their Borel subsets