MA3105 - Advanced Real Analysis - Spring term 2016

The central theme of this course is the study of certain average laws in analysis, such as the law of large numbers in probability theory and the pointwise ergodic theorem in dynamical systems. These laws describe the average behavior of say, performing the same experiment (for instance flipping a fair coin) a large number of times, or sampling an observable of a given dynamical system along a large number of iterations of a typical point.

Our preparations, applications and variations on this theme will take us through various topics in measure theory, probability theory, dynamical systems, ergodic theory, number theory.

These slides, from the student seminar talk I gave recently, offer an introduction and overview of the course.