RT1: CONnections

Manifolds are the fundamental mathematical domains underlying differential equations and dynamical systems. Élie Cartan and Shiing-Shen Chern emphasized the importance of the notion of connections on manifolds, which provide geometric information, encode symmetries, and define parallel transport as a foundation of computational algorithms for deterministic and stochastic dynamical systems. Lie group integration techniques have emerged as a superior alternative to classical coordinate-based algorithms.