Description
In this talk I will discuss a probabilistic approach to some questions in classical real algebraic geometry, like the study of the number of real zeros of real polynomial systems, or the study of the number and relative position of the connected components of a plane real algebraic curve. The main idea is to insist on the measure theoretic flavor of the notion of “generic” from complex algebraic geometry, by turning the space of polynomials into a probability space and studying the expectation of such topological quantities.
