BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Adrien Laurent DTSTART:20240503T130000Z DTEND:20240503T140000Z DTSTAMP:20260423T021650Z UID:ACPMS/40 DESCRIPTION:Title: O n the geometric and algebraic properties of stochastic backward error anal ysis\nby Adrien Laurent as part of Algebraic and Combinatorial Perspec tives in the Mathematical Sciences\n\n\nAbstract\nThe exotic aromatic exte nsion of Butcher series allowed the creation and study of integrators for the high-order sampling of the invariant measure of ergodic stochastic dif ferential equations. In particular\, the concept of backward error analysi s\, a key concept in geometric numerical integration\, seemed to generalis e in a certain sense for the study of stochastic dynamics using exotic aro matic B-series\, though there was no general result beyond order 3. In thi s talk\, we will detail the concept of backward error analysis\, quickly p resent recent results on the Hopf algebra structures related to the compos ition and substitution laws of exotic aromatic series\, and see that stoch astic backward error analysis writes naturally and at any order with exoti c aromatic B-series. Then\, we shall show that the exotic aromatic formali sm is precisely the right formalism for the formulation of backward error analysis\, thanks to a universal geometric property of orthogonal equivari ance. This is joint work with Eugen Bronasco (University of Geneva) and Ha ns Munthe-Kaas (University of Bergen and University of Tromsø).\n LOCATION:https://researchseminars.org/talk/ACPMS/40/ END:VEVENT END:VCALENDAR