Bernd Sturmfels: Varieties of signature tensors

Abstract

We discuss recent developments in combinatorial algebraic geometry that were motivated by the study of rough paths in stochastic analysis. Every path in a real vector space is encoded in a signature tensor whose entries are iterated integrals. As the path varies over a nice family, we obtain an algebraic variety with interesting properties. Combinatorialists will especially enjoy the role played by Lyndon words and free Lie algebras.