Descriptive combinatorics and the probabilistic method

Job Candidate Talk
Tuesday, February 18, 2020 - 11:00am for 1 hour (actually 50 minutes)
Skiles 005
Anton Bernshteyn – Carnegie Mellon University (CMU) – abernsht@math.cmu.edu
Lutz Warnke

Descriptive combinatorics studies the interaction between classical combinatorial concepts, such as graph colorings and matchings, and notions from measure theory and topology. Results in this area enable one to apply combinatorial techniques to problems in other (seemingly unrelated) branches of mathematics, such as the study of dynamical systems. In this talk I will give an introduction to descriptive combinatorics and discuss some recent progress concerning a particular family of combinatorial tools---the probabilistic method---and its applications in the descriptive setting.