|Speaker:||Antonio Lerario (SISSA)|
|Title:||Probabilistic Enumerative Geometry|
|Date:||Tue, Nov 14, 2017, 13:15 - 14:45|
|Place:||Seminar Room A|
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 on a generic cubic surface, the number of lines meeting four generic lines in projective space...). These problems 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, more analytical approach to these questions. This 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 works with P. Bürgisser, with S. Basu, E. Lundberg and C. Peterson and with K. Kozhasov).