Fall 2026 Calendar
A date-by-date working plan
This calendar uses McGill’s approved Fall 2026 academic dates. The content of the course is the twenty-one lectures in the notes, and the dates below give the intended pacing. Some meetings during the term are expected to be cancelled or shifted, in which case the sequence of lectures is kept and the dates move; the notes, not the dates, are the reference. The two December meetings are held in reserve to absorb such shifts. There is no midterm.
Teaching calendar
| Date | Meeting | Topic |
|---|---|---|
| Mon Aug 31 | Lecture 1 | The curse of dimensionality: integration, Monte Carlo, covers, and volume |
| Wed Sep 2 | Lecture 2 | Convex hulls and sparse approximation: Carathéodory and Maurey’s method |
| Mon Sep 7 | — | No class — Labour Day |
| Wed Sep 9 | Lecture 3 | Gaussian width: dual norms, convexification, and entropy |
| Mon Sep 14 | Lecture 4 | Tails of random variables: sub-Gaussian variables and Chernoff bounds |
| Wed Sep 16 | Lecture 5 | Geometric discrepancy and Orlicz norms |
| Mon Sep 21 | Lecture 6 | Bernstein’s inequality and dimension reduction |
| Wed Sep 23 | Lecture 7 | Coordinate embeddings |
| Mon Sep 28 | Lecture 8 | Extreme singular values I: nets and operator norms |
| Wed Sep 30 | Lecture 9 | Extreme singular values II: small-ball estimates |
| Mon Oct 5 | Lecture 10 | Extreme singular values III: rectangular sub-Gaussian matrices |
| Wed Oct 7 | Lecture 11 | Covariance estimation I: two-sided singular value bounds and the sample covariance |
| Fri Oct 9–Wed Oct 14 | — | No class — Fall Reading Break |
| Mon Oct 19 | Lecture 12 | Gaussian processes: the isonormal process and the Karhunen–Loève expansion |
| Wed Oct 21 | Lecture 13 | Gaussian concentration: Lipschitz functions, the sphere, and the Borell–TIS inequality |
| Mon Oct 26 | Lecture 14 | Gaussian comparison I: Slepian and Sudakov–Fernique |
| Wed Oct 28 | Lecture 15 | Gaussian comparison II: Gaussian matrices and Sudakov’s minoration |
| Mon Nov 2 | Lecture 16 | Gaussian width revisited: sparse vectors, random projections, and random cones |
| Wed Nov 4 | Lecture 17 | Semidefinite relaxations and max-cut: Gaussian rounding and Goemans–Williamson |
| Mon Nov 9 | Lecture 18 | Grothendieck’s inequality: the kernel trick and Krivine’s bound |
| Wed Nov 11 | Lecture 19 | Dudley’s entropy integral: chaining and sub-Gaussian processes |
| Mon Nov 16 | Lecture 20 | Applications of Dudley’s inequality: uniform laws of large numbers and Brownian continuity |
| Wed Nov 18 | Lecture 21 | Generic chaining I: the \(\gamma_2\) functional and the majorizing measure theorem |
| Mon Nov 23 | Lecture 22 | Generic chaining II: the lower bound and the matrix deviation inequality |
| Wed Nov 25 | Lecture 23 | Covariance estimation II: low-dimensional data and effective rank |
| Mon Nov 30 | Lecture 24 | Sparse recovery: the escape theorem, basis pursuit, and the Lasso |
| Wed Dec 2 | — | Reserve: catch-up for cancelled meetings, or synthesis |
| Thu Dec 3 | — | Monday make-up schedule. Reserve: catch-up or synthesis |
Academic dates
- Monday, August 31: classes begin.
- Monday, September 7: Labour Day; classes cancelled.
- Tuesday, September 15: add/drop deadline.
- Tuesday, September 22: withdrawal-with-refund deadline.
- Friday, October 9–Wednesday, October 14: Fall Reading Break; classes cancelled.
- Tuesday, October 27: withdrawal-without-refund deadline.
- Thursday, December 3: Monday-schedule make-up day.
- Friday, December 4: classes end.
- December 5–6: study days.
- Monday, December 7: examinations begin.
The official McGill calendar takes precedence if any institutional date changes.
Quiz section
Homework presentations will take place in a separate quiz section. Its day, time, and room are still to be announced, so no section meetings have been invented on this calendar. Kevin Xiao will communicate the private presenter rotation.