SFI: Structural Aspects of Signatures and Rough Paths
To start off their year at CAS, the project Signatures for Images is organising a workshop at the Centre.
Its general aim is to bring together international experts with diverse backgrounds in applied and pure mathematics to study and build the mathematical foundations for image classification using iterated-integrals and -sums signatures in the context of rough paths theory. The meeting will focus, in particular, on recent developments at the interface between algebra and geometry in the context of rough path theory. This involves, among others, pre- and post-Lie algebras (and their Lie enveloping algebras) as well as related Hopf algebras of rooted trees. Pre-Lie algebras are naturally associated with Euclidean geometry whereas post-Lie algebras encode Klein geometries, i.e., homogeneous manifolds and Lie groups. In recent years, many of these algebraic structures have found fruitful applications in the analysis of (singular) stochastic (partial) differential equations.