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>> So, I'll be speaking today about Dynamic Matching in School Choice, Efficient Seat Reassignment after Late Cancellations. This is based on joint work with Itai Feigenbaum, who is now at CUNI, and Yash Kanoria and Jay Sethuraman who are at Columbia University. >> And Yash is postdoc. >> Yes, Yash is a postdoc here. And I asked him about his experience and he said he did some of his best work while here. So, he remembers it very fondly. Give me a sec, there we go. Okay. So, let me briefly introduce you to the School Choice Problem. I don't think a School Choice as an assignment problem. We're trying to figure out how to put students in schools, but the idea is we want to let students choose where they go to school. Because maybe they have private information about which schools they prefer, which schools are better for them, maybe different students would do better at different schools. And so by using their preferences we can achieve a better assignment. So there's a theory behind how to do this assignment that was first developed by Balinsky and Sonmez, and Abdulkadiroglu and Sonmez in about 2003. It goes as follows: students have preferences, you should think of these as rank ordered lists. So, Alice prefers the Blue School, to the Orange School, to the Yellow school. On the other side of the market, we also have something we call priorities. The idea here is we're not just letting the students choose willy-nilly where they want to go to school. Maybe we also have some central objectives that we're trying to achieve, some things that we think are good from a global perspective. So, maybe we want students to be able to attend schools that are close to them, or where their siblings go. So we impose these in the form of priorities. Perhaps the students who live in the neighborhood of a school, or who have a sibling at the school, and now the goal, is to let students choose their school while respecting priorities that is- >> So, [inaudible] . But the priorities, should I think of them as real numbers that I saw after six social where there is X? >> You should think of their priorities again just as an ordinal, sort of I have equivalence classes. >> Yes. >> The equivalence classes of students. All the students who live in the neighborhood and have a sibling. All those students who just live in their neighborhood, so on and so forth. Okay. Now, we want to let students to choose their school, while respecting priorities, so students with high priority should be assigned over students with lower priority. >> All things equal. >> If this is the solution aiming for them, the theory also prescribes a way to reach it. We can run the Gale and Shapley deferred acceptance algorithm. You might know this from the context of a medical residency match, where it's used...