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.
DFG Programme
CRC/Transregios
