Acknowledgements

This work was supported by the European Research Council through the ERC project WOLF, and by the French government under the management of Agence Nationale de la Recherche as part of the “France 2030” program, reference ANR-23-IACL-0008 (PRAIRIE-PSAI).

These notes grew out of many conversations, blackboard detours, failed proofs, numerical surprises and shared mathematical obsessions. I am deeply grateful to the students, collaborators and friends. I thank Pierre Ablin; Francisco Andrade; Raphaël Barboni; Jean-David Benamou; Mathieu Blondel; Léa Bohbot; Nicolas Bonneel; Laura Cantini; Guillaume Carlier; José Antonio Carrillo; Valérie Castin; Lénaïc Chizat; David Coeurjolly; Marco Cuturi; Gwendoline De Bie; Jalal Fadili; Takashi Furuya; Alexandre Gramfort; Rémi Gribonval; Matthieu Heitz; Maarten V. de Hoop; Geert-Jan Huizing; Samuel Hurault; Hicham Janati; Jérémie Kalfon; Cyril Letrouit; Flavien Leger; Sibylle Marcotte; Arthur Mensch; Thomas Moreau; Boris Muzellec; Luca Nenna; Clarice Poon; Julien Rabin; Zakaria Ramzi; Pierre Roussillon; Jules Samaran; Michael Sander; Meyer Scetbon; Othmane Sebbouh; Justin Solomon; Thibault Séjourné; François-Xavier Vialard; Zhenzhang Ye; and Kelvin S. Zhang. Their ideas, taste, questions and generosity have shaped the mathematical atmosphere in which this book was written.

Finally, my deepest and most personal thanks go to my three children, Mael, Camille and Arthur, and to my love, Gwenn Guichaoua. I am lucky to share with her a passion for mathematics, computer science and biology.