Séminaire Géométries ICJ

Probabilistic enumerative geometry

par Antonio Lerario

Europe/Paris
Salle 112 (ICJ)

Salle 112

ICJ

1er étage bâtiment Braconnier, Université Claude Bernard Lyon 1 - La Doua
Description
A classical problem in enumerative geometry is the count of the number of linear spaces satisfying some geometric conditions (e.g.​ ​the number of lines meeting four generic lines in projective space). ​P​roblems ​​of this type are usually approached with the technique of Schubert Calculus, which describes how cycles intersect in the Grassmannian. In this talk I will present a ​novel approach to these questions​ which comes after adopting a probabilistic point of view―the main idea is the replacement of the word generic with random. Of course over the complex numbers this gives the same answer, but it also allows to compute other quantities especially meaningful over the reals, where the generic number of solutions is not defined (e.g. the signed count or the average count). (This is based on joint work​​ with ​P. Bürgisser)