Title: Enumerative geometry: from Ancient Greeks to Modern Physicists
Apollonius of Perga asked: how many circles are tangent to 3 given circles in the plane? This is a typical problem of enumerative geometry. The subject saw great advances in the 19th century under the influence of Schubert, but certain problems remained unsolved, such as the determination of the number of rational curves of degree d through 3d-1 general points in the plane for arbitrary d. In the 20th century, new invariants of algebraic varieties were discovered such as Gromov-Witten invariants, which play a role in string theory. Kontsevich used these invariants to solve this longstanding problem. I will give a \emph{non-technical} overview of some of the history of enumerative geometry with an eye towards recent developments. Links with topology are discussed.
Location: KdVI meeting room, Science Park 105-107, F3.20