Alessio Figalli: Regularity theory of optimal transport maps. Teil 2 Mitschnitt einer Veranstaltung des Erwin Schrödinger International Institute for Mathematics and Physics (ESI) am Montag, dem 13. Mai 2019 im Boltzmann-Hörsaal des ESI Kamera und Schnitt: Viktor Zdrachal Alessio Figalli ist Professor Department of Mathematics an der ETH Zürich. Abstract: The aim of this lecture is to present the regularity theory for optimal maps, explaining the connection to Monge-Ampère type equations and giving an overview of the most fundamental results available on this important topic. INHALT ====== Kapitel Titel Position --------------------------------------------------------------------- 1. Vorspann 00:00:00 2. The question of regularity 00:00:24 3. Non-convex targets. The singular set 00:13:50 4. Caffarelli's contraction theorem 00:23:52 5. Evaluation at the maximum point x = x̄ 00:36:19 6. Application: Poincaré inequalities 00:43:38 7. General cost 00:50:50 8. Questions from the audience 01:00:30

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