The topic is differential equations (both partial and ordinary differential equations).
Unless otherwise noted, talks are Thursdays, 13:15–14:00 in room 734, S-2.
| Date | Speaker | Title |
|---|---|---|
| 2007-11-01 13:15–14:00 |
Fabio Priuli | Optimal transportation (part 5 of n)
(Abstract:
To conclude the second chapter of Villani's book,
we will focus on optimal plans in R,
trying to make the characterization of optimal
transportation plans a bit clearer, and we will
show what is known (at the present stage of the
research) about the general case of Polish
spaces X, Y and lower semicontinuous costs
c(x,y).) |
| 2007-09-13 13:15–14:00 |
Xavier Raynaud and Fabio Priuli | Optimal transportation (part 1 of n)
(Abstract: Following the book of Villani (Topics in Optimal Transportation, Graduate Studies in Mathematics, American Mathematical Society, Providence, 2003), we will give a short presentation of the theory of optimal transportation and some of its connections with partial differential equations. Our plan is to continue with a series of short lectures (taking place during the DIFTA seminar when no seminar is scheduled) where we will go in more details through some selected results.) |
| 2007-09-20 13:15–14:00 |
Xavier Raynaud | Optimal transportation (part 2 of n)
(Abstract: We start with the first chapter of Villani's book, which deals with duality. We will prove the existence of a minimizer for the optimal transportation problem and then start the proof of the Kantorovich duality. Some of the ingredients: a compactness theorem on the space of probability measure (Prokhorov theorem), and a “minimax” principle (“inf sup = sup inf”) from convex analysis.) |
| 2007-09-27 13:15–14:00 |
Kristian Debrabant | Runge–Kutta methods for stochastic differential equations (abstract) |
| 2007-09-20 12:15–14:00 |
Xavier Raynaud | Optimal transportation (part 3 of n)
(Abstract:
We finish the proof of the existence of a
minimizer and go through the duality theory
(Theorem 1.3 in the book).) |
| 2007-10-25 12:30–14:00 |
Fabio Priuli | Optimal transportation (part 4 of n)
(Abstract:
We start the second chapter of Villani's book,
which deals with a characterization of optimal
transportation plans. We will introduce a few
concepts from convex analysis and prove that,
for measures with finite second moments, any
optimal transportation plan is related to the
subdifferential of a convex function. Finally,
we will focus on optimal plans in R,
trying to make the characterization a bit clearer.) |