22 feb 2019 -- 12:00
Sala Tricerri, DiMaI, Firenze
Abstract.
Over the past few years there has been an intense activity around the field of "Random Algebraic Geometry", whose main interest has been studying the zero set of random real algebraic equations. The main idea of this study is to approach real algebraic geometry replacing the notion of "generic", from complex algebraic geometry, with the notion of "random". In this talk I will adopt this philosophy for the study of properties of real tensors. For example: what is the expected real rank of a random symmetric tensor? The answer to this question is related to the volume of the secant locus of the Veronese variety (alternatively: to the number of multiple points of a random rational map...) I will present recent results on the subject of random tensor geometry, trying to explain some general principles and discussing why, in the large degree limit, random real algebraic geometry behaves as the "square root" of complex algebraic geometry.