Maxwell Institute for Mathematical Sciences

Geometric inverse semigroup theory: a note on the Milnor–Schwarz lemma for inverse monoids

Abstract We generalise the Milnor–Schwarz lemma to inverse monoids acting on presheaves of geodesic metric spaces. We provide two proofs of this fact: one only uses elementary techniques, inspired by the arguments for group actions on metric spaces; the other involves a version o...

Stochasticity and probabilistic trajectory scoring are essential for data-driven closures of chaotic systems

Coarse-grained models of chaotic systems neglect unresolved degrees of freedom, inducing structured model error that limits predictability and distorts long-term statistics. Typical data-driven closures are trained to minimize prediction error over a single time step, implicitly...

Normal forms of elliptic automorphic Lie algebras and Landau–Lifshitz type of equations

Abstract We present normal forms of elliptic automorphic Lie algebras with dihedral symmetry of order 4, which arise naturally in the context of Landau–Lifshitz type of equations. These normal forms provide a transparent description and allow a classification of such Lie algebras...