Abstract : 

I will talk about maps with minimal distortion between surfaces, a theory started by W. P.  Thurston's in his paper ``Minimal stretch maps between hyperbolic surfaces", who used these maps in the definition of a new metric on Teichmüller space, now called the Thurston metric. I will survey recent works on this topic in various settings (Euclidean, non-Euclidean and mixed). I will mention relations with physics, biology and art.

Athanase Papadopoulos is Directeur de Recherche at the French Centre National de la Recherche Scientifique (France) working at the Institut de Recherche Mathématique Avancée (Strasbourg). His main fields of interest are geometry and topology and he also publishes on the history and philosophy of mathematics, on acoustics and on music theory. He has held visiting positions at the Institute for Advanced Study, Princeton (1984–85 and 1993–94), USC (1998–1999), CUNY (Ada Peluso Professor, 2014), Brown University (Distinguished visiting professor, 2017), Tsinghua University, Beijing (2018), Lamé Chair of the State University of Saint Petersburg (2019),  Galatasaray University (Istanbul), the University of Florence (Italy), Fudan University (Shanghai), Gakushuin University (Tokyo), Presidency University (Calcutta) and Banaras Hindu University. In 2025, he delivered the GIAN course at Jawaherlal Nehru University (Delhi). He is the author of more than 220 published articles and about 50 monographs and edited books.