Classes start on Sep 24 and continue through Dec 5.
Classes will be taught remotely on MWF and there will be in-person office hours at UBC and UW for further discussion. UW students can register for this course under the number Math 581 C.
Class times:
This course will be taught in a hybrid manner. This course is taught by two instructors YK and SP. The class time will depend on who teaches the individual class. Nevertheless, there will be three 90 mins lectures per week. Videos of the lectures will be put on YouTube and notes will be distributed to students over Slack.
Zoom links:
If you are registered for this class you will be added to the course Slack where you can find the Zoom link. If you are auditing, please send an e-mail to the instructors and we will add you to the Slack workspace where again you will find the Zoom link. Please do not share the Zoom link without asking us.
Lecture times MWF 11:00 am – 12:30 pm
When YK teaches it will be hybrid (in-person at GEOG 109 in UBC + online). YH's in-person office hours will be announced later.
When SP teaches it will be online. Additionally SP will provide in-person office hours on Tuesdays from 1-3 pm at Padelford C-547.
Online zoom link: You can find it in the course Slack workspace.
Slack: This is for communications between students and instructors. You should get an invitation if you are registered. Otherwise send us an e-mail.
Grading will be based on class participation. Optional exercises will be provided.
The following is the list of holidays: Oct 10, 13 (Canadian Thanksgiving), Nov 26, 28 (US Thanksgiving)
Course calendar and syllabus (subject to changes):
Week 1: YH teaches.
Wed, Sep 24 - Statement of the OT problem. Existence of solutions.
Fri, Sep 26 - Linear programming. Duality.
Week 2: YH teaches.
Mon, Sep 29 - Kantorovich Duality I: Role of convexity.
Wed, Oct 1 - Kantorovich Duality II: Dual attainment.
Fri, Oct 3 - Brenier's Theorem
Week 3: SP teaches.
Mon, Oct 6 - geodesics, generalized geodesics, displacement interpolation.
Wed, Oct 8 - geodesic convexity, generalized geodesic convexity
Week 4: SP teaches
Wed, Oct 15 - absolutely continuous curves and continuity equations.
Fri, Oct 17 - Benamou-Brenier dynamic formulation of OT.
Week 5: YH teaches
Mon, Oct 20 - 2-Wasserstein space as a geodesic metric space.
Wed, Oct 22 - Gangbo-McCann theorem.
Fri, Oct 24 - Monge-Ampère equation.
Week 6: YH teaches
Mon, Oct 27 - Otto calculus. Tangent spaces.
Wed, Oct 29 - Wasserstein gradients
Fri, Oct 31 - Gradient flows and diffusions
Week 7: SP teaches.
Mon, Nov 3 - JKO scheme and gradient flows
Wed, Nov 5 (Special lectures)
Fri, Nov 7 (Special lectures)
Week 8: SP teaches.
Mon, Nov 10 - Langevin diffusions as gradient flows
Wed, Nov 12 - Log-Sobolev and other functional inequalities
Fri, Nov 14 - Entropic regularization of OT
Week 9. SP teaches.
Mon, Nov 17 - Schrödinger bridges
Wed, Nov 19 - Mirror gradient flows and mirror Langevin diffusions
Fri, Nov 21 - Mirror gradient flows and parabolic PDEs
Week 10. YH teaches
Mon, Nov 24 - Wasserstein barycenters
Week 11. YH teaches
Mon, Dec 1 - Unbalanced OT
Wed, Dec 3 - TBD
Friday. Dec. 5. TBD