Schedule | 21-317 Functional Inequalities
21-317 · Fall 2026
Schedule
The provisional meeting-by-meeting calendar for the instructor-led bridge, three rounds of student presentations, and end-of-semester workshops.
Updated September 19 Round I runs September 28–October 19. Topics and speaker order are unchanged; later-round dates remain provisional.
Calendar assumptions
This calendar reflects the current enrolment of seven students and three presentation rounds, with one presentation by each student in each round. The instructor-led bridge continues through September 25. Round I begins September 28 and ends October 19, the first class after Fall Break. The September 19 revision shifts the programme one class meeting later through November 16: the October 30 synthesis/workshop moves to November 2, and the former November 16 workshop is removed. Presentations on November 18, 20, and 23 and the end-of-semester workshops retain their dates. The presentation order varies between rounds to distribute preparation time. Round I topic assignments and each round’s speaker order are unchanged; later-round dates remain provisional. Paper milestones will be announced separately on Canvas. The university calendar lists 13 Monday, 13 Wednesday, and 13 Friday class meetings for Fall 2026.
| Week | Date | Meeting |
|---|---|---|
| 1 | Bridge 1: Panorama—why should a function be almost constant? | |
| 1 | Bridge 2: Finite probability | |
| 1 | Bridge 3: Entropy and Gibbs equilibrium | |
| 2 | Bridge 4: Finite-state Markov chains | |
| 2 | Bridge 5: Continuous-time Markov chains and semigroups | |
| 2 | Bridge 6: Stationarity, detailed balance, and reversibility | |
| 3 | No class: Labor Day | |
| 3 | Instructor-led bridge: Dirichlet edge energy for continuous-time Markov chains | |
| 3 | Instructor-led bridge: Poincaré inequality, spectral gap, Rayleigh quotient, and variance decay | |
| 4 | Instructor-led bridge: Measure and integration as needed | |
| 4 | Instructor-led bridge: Weak derivatives, Sobolev spaces, and periodic Poincaré | |
| 4 | Instructor-led bridge: Sobolev, isoperimetric, and Nash inequalities | |
| 5 | Instructor-led bridge: Logarithmic Sobolev inequalities, entropy decay, tensorisation, and concentration | |
| 5 | Instructor-led bridge and Round I preparation | |
| 5 | Instructor-led bridge and Round I preparation | |
| 6 | Round I — Yizhou Li Topic 06: Gaussian Poincaré inequality via the Ornstein–Uhlenbeck semigroup |
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| 6 | Round I — Rohan Mecheri Topic 02: Random walk on a cycle and diffusive relaxation |
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| 6 | Round I — Justin Blanco Topic 01: Sharp Poincaré inequalities and boundary conditions |
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| 7 | Round I — Oliver Yao Topic 07: Logarithmic Sobolev inequalities and the Herbst argument |
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| 7 | Round I — Sudais Arif Topic 04: Cheeger inequality and bottlenecks on regular graphs |
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| 7 | Round I — Sarah Yildirim Topic 03: Tensorization of variance and the Efron–Stein inequality |
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| 8 | No class: Fall Break | |
| 8 | No class: Fall Break | |
| 8 | No class: Fall Break | |
| 9 | Round I — Amber Zhang Topic 10: Entropy, likelihood, and Gibbs equilibrium |
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| 9 | Round II — Oliver Yao | |
| 9 | Round II — Sudais Arif | |
| 10 | Round II — Sarah Yildirim | |
| 10 | Round II — Amber Zhang | |
| 10 | Round II — Rohan Mecheri | |
| 11 | Instructor-led synthesis and workshop | |
| 11 | Round II — Yizhou Li | |
| 11 | Round II — Justin Blanco | |
| 12 | Round III — Sudais Arif | |
| 12 | Round III — Sarah Yildirim | |
| 12 | Round III — Amber Zhang | |
| 13 | Round III — Rohan Mecheri | |
| 13 | Round III — Yizhou Li | |
| 13 | Round III — Justin Blanco | |
| 14 | Round III — Oliver Yao | |
| 14 | No class: Thanksgiving Break | |
| 14 | No class: Thanksgiving Break | |
| 15 | Expository-paper workshop | |
| 15 | Instructor synthesis and capstone discussion | |
| 15 | Course synthesis and reflection; last day of classes |
This schedule supersedes the four-round provisional calendar in syllabus version 0.2, dated August 24, 2026. The September 18 revision established seven presentations per round; the September 19 revision moves the start of Round I to September 28 and removes the November 16 workshop, without changing topics or speaker order. Later changes will be posted on this page and in the announcement archive.