Lecture notes for 390B.
All Lectures to date.

Unitary representations:
 Group actions on measure spaces:
 Uniform multiple recurrence:
Lecture 1 - Definitions and constructions.
 Lecture 11 - Examples.
 Lecture 18 - Multiple recurrence for compact actions.
Lecture 2 - Functions of positive type.
 Lecture 12 - The Koopman representation.
 Lecture 19 - Multiple recurrence for weak mixing actions.
Lecture 3 - Cocycles.
 Lecture 13 - A remark about measure spaces.
 Lecture 20 - Joinings.
Lecture 4 - Induced representations.
 Lecture 14 - Gaussian actions.
 Lecture 21 - The basic construction.
Lecture 5 - Invariant vectors.
 Lecture 15 and 16 - Ergodic theorems.
 Lecture 22 - Ergodic, weak mixing, and compact extensions.
Lecture 6 - Amenability.
 Lecture 17 - Recurrence theorems.
Lecture 7 - Mixing properties.
Lecture 8 - Compact representations.
Lecture 9 - Weak mixing for amenable groups.
Lecture 10 - Weak containment.