Professor: Katy Craig, katy•craig at ucsb • edu

Lecture: Tuesday and Thursday, 9:30-10:45am

Lecture Location: HSSB 2251

Office Hours: Thursday 11am-12pm, Friday 1-2pm, and by appointment

Optimal Transport Wiki: otwiki.xyz

Recommended References:

• Functional Analysis:
  Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations,
• Convex Analysis:
  Bauschke and Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces,
• Fluid Mechanics and PDEs:
  Chorin and Marsden, A Mathematical Introduction to Fluid Mechanics,
• Optimal Transport:
  Villani, Topics in Optimal Transportation,
  Santambrogio, Optimal Transport for Applied Mathematicians,
  Figalli, Glaudo, An Invitation to Optimal Transport,
  Ambrosio, Brué, Semola Lectures on Optimal Transport,
  
• Gradient Flows:
  Ambrosio, Gigli, Savaré, Gradient Flows in Metric Spaces and in the Space of Probability Measures,
  Ambrosio and Savaré, Gradient Flows of Probability Measures,
  Santambrogio, {Euclidean, metric, and Wasserstein} gradient flows,
  
• Computational Optimal Transport:
  Peyré and Cuturi, Computational Optimal Transport,
  
• Statistical Optimal Transport:
  Chewi, Niles-Weed, and Rigollet, Statistical Optimal Transport,
  

Exams: none.

Homework:

• The main assignment will be to work together to continue building the Optimal Transport Wiki: otwiki.xyz.
  
  • Jan 31st: Select a topic on which you will write a new article for the wiki. Create a new page for your topic and include your name in the page's title, to indicate that you have chosen this topic. (Example: "Kantorovich Problem - Katy Craig")
  • Feb 14th: Finish your expository article for the wiki. After I review your article, I will remove your name from the title.
  • Feb 21st: Select an existing wiki article, for which you will complete a major revision. Add your name to the end of the article's title, to indicate that you have chosen this article to revise.
  • March 7th: Complete a major revision of an existing article for the wiki. After I review your revision, I will remove your name from the title.
  For each article you work on, please include citations to all references you used in preparation of the article. Here is a short video explaining how to create a new article on the wiki.
  
  
• As a smaller assignment, each student will type up a detailed solution to two or three of the exercises I give in class. Solutions should be typed in the shared Overleaf document linked below. To indicate that you have selected a solution to work on, please type your name after the word ``Solution'' in the shared Overleaf file. Solutions should be submitted within one week of when the exercise was assigned.

The above deadlines are chosen to help prevent you from getting behind. All deadlines are flexible, though all work (including revised work, submitted for a regrade), must be submitted by March 14th. If you would like to submit revised work, keep it mind that it typically takes me a week to provide feedback on the original version.

Grading Scheme: First article: 30%, Second article: 30%, Exercise Solution(s) 10%, Class participation: 30%

Prerequisites: Measure theory, functional analysis

Exercises: List of homework exercises and solutions

Syllabus:

		topic	lecture notes
1	Jan 7 (T)	the optimal transport problem and transport of measures	LEC1
2	Jan 9 (Th)	normalizing flows and the Monge problem	LEC2
3	Jan 14 (T)	from transport maps to transport plans	LEC3
4	Jan 13 (Th)	the Kantorovich problem	LEC4