Course Descriptions

16:640:569 - Selected Topics in Logic

Simon Thomas

Subtitle: 

Borel Equivalence Relations

Text:

Notes

Prerequisites:

Familiarity with the basic theory of complete separable metric spaces and their Borel subsets

Course Description:

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.

 

Fall 2017

Simon Thomas

Subtitle: Countable Borel Equivalence Relations

Course Description:

This course will be an introduction to countable Borel equivalence relations, a very active area of classical descriptive set theory which interacts nontrivially with such diverse areas of mathematics as model theory, computability theory, group theory and ergodic theory. The topics to be covered will include applications of superrigidity theory to countable Borel equivalence relations, as well as some recent applications of Borel determinacy. No prior knowledge of superrigidity or determinacy will be assumed.

 Text: 

None

Prerequisites:

Familiarity with the basic theory of complete separable metric spaces and their Borel subsets

Schedule of Sections:

For more information on instructors and sections for Fall 2017, please see our Fall 2017 Teaching Schedule Page

For more information on instructors and sections for this course for other semesters, please see our Teaching Schedule Page