## Trjitzinsky Memorial Lectures

October 10-12, 2017

### A descriptive set theoretic approach to problems

in harmonic analysis, ergodic theory and combinatorics

### presented by

### Alexander Kechris, Caltech

Descriptive set theory is the study of definable sets and functions in Polish (complete, separable metric) spaces, like, e.g., the Euclidean spaces. It has been a central area of research in set theory for over 100 years. Over the past three decades, there has been extensive work on the interactions and applications of descriptive set theory to other areas of mathematics, including analysis, dynamical systems, and combinatorics. My goal in these lectures is to give a taste of this area of research, including an extensive historical background.

These lectures require minimal background and should be understood by anyone familiar with the basics of measure theory and functional analysis. Also the three lectures are essentially independent of each other.

Lecture I. 4 pm, 314 Altgeld Hall, October 10, 2017

Set theory and trigonometric series

A reception will be held from 5-6 pm in 239 Altgeld Hall.

Lecture II. 4 pm, 245 Altgeld Hall, October 11, 2017

The complexity of classification problems in ergodic theory

Lecture III: 4 pm, 245 Altgeld Hall, October 12, 2017

Descriptive graph combinatorics