MATH 598 / 784 · Fall 2026

High-Dimensional Probability

Meetings

Lectures: Monday and Wednesday, 10:05–11:25, Burnside Hall 920
Instructor: Elliot Paquette
Homework coordinator and reader: Kevin Xiao

The first lecture is Monday, August 31. The final Monday-schedule meeting is held on Thursday, December 3, following McGill’s make-up-day convention. See the calendar for the full teaching plan.

Notes

The mathematical notes are organized as durable lectures rather than as a transcript of what happened in the room. The course covers the following twenty-one lectures, which together form the complete content of the term. Some lectures occupy more than one meeting, and the calendar records the intended pacing.

  1. The Curse of Dimensionality
  2. Convex Hulls and Sparse Approximation
  3. Gaussian Width
  4. Tails of Random Variables
  5. Geometric Discrepancy and Orlicz Norms
  6. Bernstein’s Inequality and Dimension Reduction
  7. Coordinate Embeddings
  8. The Smallest and Largest Singular Values
  9. Covariance Estimation
  10. Gaussian Processes
  11. Gaussian Concentration
  12. Gaussian Comparison and Gaussian Matrices
  13. Gaussian Width Revisited
  14. Semidefinite Relaxations and Max-Cut
  15. Grothendieck’s Inequality
  16. Dudley’s Entropy Integral
  17. Applications of Dudley’s Inequality
  18. Generic Chaining
  19. The Lower Bound and the Matrix Deviation Inequality
  20. Covariance Estimation for Low-Dimensional Data
  21. Sparse Recovery

Exercises and quiz section

Students should work on every problem in each exercise sheet. In the separate quiz section, students will take turns presenting assigned problems; a student need only present when it is their turn, but should be ready to discuss all of the problems.

Kevin Xiao will coordinate the private presentation rotation and read the homework. If a student is exceptionally unable to give an assigned presentation in the quiz section, the presentation must be made independently to Kevin. Presenter names will not appear on this public website.

The quiz-section day, time, and room will be announced. The first exercise sheet will be discussed Friday, September 11.

Assessment

The assessment weights are still being finalized. There is no midterm; the calendar uses every meeting for lectures.

Working character of the course pages

The lecture notes are intended to become evergreen. Dates, rooms, homework procedures, and assessment information on pages under Course apply only to the Fall 2026 offering and may be revised during internal course preparation.