MA 363: Probability in High Dimensions (Spring 2021)
Instructor: Anirban Basak 
Email: anirban.basak@icts.res.in 
Office hours: Online. By email appointment. 
Class time and location: TuTh 10.0011.30 AM. Lectures will be held over Zoom. Interested students are requested to email to get the meeting link. First class is on March 02. 
Prerequisite: This is a graduate level topics course in probability theory. Graduate level measure theoretic probability will be useful, but not a requirement. Students are expected to be familiar with basic probability theory and linear algebra. The course will be accessible to advanced undergraduates who have had sufficient exposure to probability and linear algebra. 
Course outline: This course will be aimed at understanding the behavior of random geometric objects in high dimensional spaces such as random vectors, random graphs, random matrices, and random subspaces, as well. Topics will include the concentration of measure phenomenon, nonasymptotic random matrix theory, empirical processes, and some related topics from geometric functional analysis and convex geometry. Towards the latter half of the course, depending on students' interests, a few applications of the topics covered in the first half will be considered such as community detection, covariance estimation, randomized dimension reduction, and sparse recovery problems. 
Suggested books and references: 
Schedule of topics covered and lecture notes:

Problem Set (to be updated regularly): See here
Grading: Students taking this course for credit are required to do either of the following: 1) Solve at least 60% of the problems assigned during the lectures, or 2) Do a (reading) project, submit a report, and give a presentation on the same at the end of the semester. The final grade will be based primarily on the basis of efforts.