Causal reasoning is usually formalized through structural causal models (SCMs) or potential outcomes. These frameworks have been enormously successful for modeling, identification, and inference, but they are not primarily designed as axiomatic foundations analogous to probability spaces in probability theory. This tutorial introduces causal spaces, a measure-theoretic framework in which interventions are represented by primitive causal kernels satisfying two minimal axioms: doing nothing leaves everything unchanged, and intervened coordinates take their prescribed values. The tutorial will explain the motivation for causal spaces, present the basic definition and semantics, and work through examples linking back to familiar causal models. It will then present some further development of basic causal space theory, such as causal effects, sources, identifiability, and counterfactual spaces, and touch upon advanced topics such as targeted interventions and continuous-time stochastic processes that are more difficult to express in existing frameworks.

"The talk addresses the quantitative study of resilience in dynamical systems by analyzing a range of resilience indicators within a unified mathematical and computational framework. Emphasis is placed on ecological resilience and on extending existing approaches from autonomous systems to settings with time-dependent perturbations, leading to nonautonomous dynamics. To address the lack of classical invariant structures in this context, characteristic performance ranges are used as practical reference states. The developed framework is applied to case studies, demonstrating how time-dependent disturbances and rate-induced effects influence resilience and tipping behavior."