Lecture 1: Introduction to Analysis on the Discrete Cube I
Lecture 2: Introduction to Analysis on the Discrete Cube II
Lecture 3: Introduction to Analysis on the Discrete Cube III
Lecture 4: Introduction to Analysis on the Discrete Cube IV

This series of talks was part of the Real Analysis Boot Camp. Videos for each talk are available through the links above.

Speaker: Krzysztof Oleszkiewicz (University of Warsaw)
The basic notions and ideas of analysis on the discrete cube will be discussed, in an elementary and mostly self-contained exposition. These include the Walsh-Fourier expansion, random walk and its connection to the heat semigroup, hypercontractivity and related functional inequalities, influences, the invariance principle and its application to the Majority is Stablest problem. The mini-course will also contain some other applications and examples, as well as several open questions.