A Tale of Three Structures: the Arithmetics of Multizetas, the Analysis of Singularities, the Lie algebra ARI (original) (raw)

Two new, fast-developing, but at first sight completely diconnected subjects have turned out to be governed by a common underlying structure. These two subjects are : the specific singularities, Stokes phenomena and resurgence patterns exhibited by singularly perturbed systems ; and the phenomenon of dimorphy (existence of a double product) displayed not only by the so-called multizeta values but by a host of other basic transcendental constants. As for the unifying structure, it is the novel Lie algebra ARI which, together with its group GARI and a number of related constructions, is a fascinating object in its own right. 3 Singularly perturbed systems and co-equational resurgence. 3.1 Some heuristics: similarities/differences between SS and SPS. .