Lecture Series (5 lectures)

These talks are not intended to geometers. There will be no attempt to provide any global view of geometry today. My intention is to present five old papers which have been influential in the later development of geometry. In each case, I’ll try to focus on the motivations of these pioneers which are almost always related to applied mathematics : a reminder for contemporary geometers? In each case, I’ll try to mention a few forgotten problems which might be relevant today. These five talks will be completely independent and hopefully elementary. 1- Monge and optimal transport (1776) 2- Gauss and cartography (1825) 3- Hadamard and geodesics of negatively curved surfaces (1898) 4- Poincar´e and geodesics of positively curves surfaces (1905) 5- Birkhoff and the ergodic theorem (1931)