Project A05
Signatures at the threshold of analysis, algebra and geometry: new perspectives

Project description

Path signatures, pivotal in rough path theory, are formal power series or tensor series, influenced by algebraic and geometric structures. This project is dedicated to the algebraic and geometric features of signatures, focusing on the structure of paths they describe and the groups they generate. We explore Euler-Maclaurin formulas in a Young-Stieltjes and rough path setting, smooth rough paths as Cartan developments, classifying processes with finite signature cumulants, and the infinite-dimensional geometry of groups of tree-reduced paths. 

Principal Investigators

Peter Friz (TU Berlin)

Sylvie Paycha (U Potsdam)

Project members

Felix Medwed (U Potsdam)

Matteo Ravot Licheri (TU Berlin)

Publications

• Friz, P.K., Lyons, T., Seigal, A., 2024. Rectifiable paths with polynomial log‐signature are straight lines. Bulletin of London Math Soc 56, 2922–2934. https://doi.org/10.1112/blms.13110 

Preprints

• Friz, P. K., Hager, P. P., 2025. Expected Signature Kernels for Lévy Rough Paths. https://doi.org/10.48550/ARXIV.2509.07893 (A02, A05)