Rough Flow techniques on manifolds

Abstract: In 2020, Armstrong et al managed to explicitly write down Davie’s formula of the solution of a non-geometric RDE on a manifold for the level N = 2. In this talk, we introduce a new notion, called pseudo bialgebra map, which allows us to construct similar expansions for higher level rough pahs living in general Hopf algebras. To do this, we prove a local version of Bailleul’s sewing lemma for flows. Finally, we go over previous results and show that they do give rise to pseudo bialgebra maps. Based on joint work with Terry Lyons.

machine learningcommutative algebraalgebraic geometryalgebraic topologycombinatoricscategory theoryoperator algebrasrings and algebrasrepresentation theory

Audience: researchers in the topic

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Algebraic and Combinatorial Perspectives in the Mathematical Sciences

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