Reading course

  • Lecture 1 (Massimiliano Datres), 2022-03-16, 9.30-11.30 room Seminar -1: pag 2-8 (introduction, Monge, Kantorovich, Existence of transport plans) (Video)
  • Lecture 2 (Francesco Menegale) 2022-03-23, 9.30-11.30 room Seminar -1: pag 9-10 (transport 1-d, discrete transport) (Video)
  • Lecture 3 (Simone Verzellesi) 2022-03-30, 9.30-11.30 room Seminar -1: pag 19-29 (Kantorovich and Fenchel-Rockafellar duality, existance of the dual problem) (Video)
  • Lecture 4a: (Simone Verzellesi) 2022-04-06, 9.30-10.00 room 7 (Video)
  • Lecture 4b: (Gabriele Morselle) 2022-04-06, 10.00-11.30 room 7: pag 30-36 (introduction to the Knott-Smith criterion, Brenier theorem, prerequisites) (Video)
  • Lecture 5: (Francesco Menegale) 2022-04-13, 9.30-10.30 room 7: pag 36-40 (Knott-Smith and Brenier proofs) (Video)
  • Lecture 6: (Simone Verzellesi) 2022-04-20, 9.30-10.30 room 7: pag 41-46 (introduction to Wasserstein distance) (Video)
  • Lecture 7: (Massimiliano Datres) 2022-4-27, 9.30-11.30 room 7: pag 46-51 (Wasserstein topology, geodesics) (Video)
  • Lecture 8: (Giacomo Vianello) 2022-05-04, 9.30-11.30 room 7: A proof of the isoperimetric inequality via optimal transport (Video)
  • Lecture 9: (Gabriele Morselli) 2022-05-18, 9.30-11.30 room 7: Figalli, Maggi, Pratelli (2010) A mass transportation approach to quantitative isoperimetric inequalities. Invent. Math. 182 (1), 167-211. (Video)
  • Lecture 10: (Gianmarco Caldini) 2022-05-25, 9.30-11.30 room 7: Optimal branched transport (Video)

Reference

Other References

  • Brancolini, Buttazzo, Santambrogio (2006) Path functionals over Wasserstein spaces. J. Eur- Math. Soc. 8(3), 415-434.
  • Gromov’s proof of the anisotropic isoperimetric inequality. In: Milman, V.D., Schechtman, G.: Asymptotic Theory of Finite-dimensional Normed Spaces. With an appendix by M. Gromov. Lecture Notes in Mathematics.
  • Cordero-Erausquin, D., Nazaret, B., Villani, C. (2004) A mass-transportation
    approach to sharp Sobolev and Gagliardo-Nirenberg inequalities. Adv. Math. 182(2), 307-332.

Details

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