Course Identification
Lattices and Random Groups
Lecturers and Teaching Assistants
Prof. Tsachik Gelander
Course Schedule and Location
Second Semester
Tuesday, 11:15 - 14:00, Ziskind, Rm 155
29/03/2022
Field of Study, Course Type and Credit Points
Mathematics and Computer Science: Lecture; Elective; Regular; 3.00 points
Prerequisites
Lie groups and Lie algebras.
Attendance and participation
Estimated Weekly Independent Workload (in hours)
Syllabus
1. Basic Notions in the Theory of Lattices and Arithmetic Groups
2. Invariant Random Subgroups (IRS)
3. Stationary Random Subgroups (SRS)
Learning Outcomes
Upon successful completion of this course students should be able to:
We will focus on probabilistic techniques to study discrete subgroups of Lie groups and in particular arithmetic groups and asymptotic invariants of such. We will develop the theory of invariant random subgroups (IRS) as well as non-invariant stationary random subgroups (SRS).
Reading List
Literature:
1. Raghunatan - Discrete subgroups of lie groups
2. Margulis - Discrete subgroups of semisimple lie groups
3. Gelander - Lectures on Invariant Random Subgroups