Optimal transport theory was introduced at the end of the 18th century by Gaspard Monge, to understand the most efficient way of transporting a distribution of material from one place to another to build fortifications. In the last 30 years, this theory has found various applications in many problems, both from nature and machine learning. In this talk, I will present some of the applications that have been most relevant in my research.
Alessio Figalli earned his doctorate in 2007 under the supervision of Luigi Ambrosio at the Scuola Normale Superiore di Pisa and Cédric Villani at the École Normale Supérieure de Lyon.
He was a faculty at University of Texas-Austin, before moving to ETH Zürich in 2016 as a chair professor. Since 2019 he is the director of the “FIM-Institute for Mathematical Research” at ETH Zürich.
Figalli has won an EMS Prize in 2012, the Peccot-Vimont Prize in 2011, the Peccot 2012 of the Collège de France, the Stampacchia Medal in 2015, and the Feltrinelli Prize for mathematics in 2017, and has been appointed Nachdiplom Lecturer in 2014 at ETH Zürich. He was an invited speaker at the International Congress of Mathematicians in 2014.
In 2018 he won the Fields Medal for “his contributions to the theory of optimal transport, and its application to partial differential equations, metric geometry, and probability”.