BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lucas Broux (SISSA) DTSTART:20260205T130000Z DTEND:20260205T150000Z DTSTAMP:20260423T004038Z UID:PSMQFT/5 DESCRIPTION:Title: A geometric view upon the renormalisation of stochastic PDEs: the example o f $\\Phi^4$\nby Lucas Broux (SISSA) as part of Probability\, Statistic al Mechanics and Quantum Fields\n\nLecture held in 004 via Bonomea 265\, S ISSA.\n\nAbstract\nIn this talk\, I wish to present some ideas concerning the well-posedness of the $\\Phi^4$ equation\, which is a stochastic parti al differential equation (SPDE) with a cubic nonlinearity and perturbed by an additive random (and rough) noise. More precisely\, we are interested in the range of noises where this SPDE is singular (i.e. is classically il l-posed) but subcritical (i.e. the nonlinearity formally vanishes at small scales). In this range\, even giving a meaning to the equation is highly non-trivial and relies on an appropriate procedure of regularisation and r enormalisation\, as was first understood by Da Prato and Debussche (2003) and later widely generalised by several approaches including Hairer's theo ry of regularity structures (2014).\nI will\, on the one hand\, introduce some of the important insights in the theory of singular SPDEs\, and\, on the other hand\, present some more recent contributions. In particular\, I will be describing how taking a geometric viewpoint upon the solution man ifold gives rise to a new perspective on what in the theory of regularity structures is called a ``model'' for the equation. If time permits\, I wil l also briefly present a recently-developed ``intrinsic'' approach for the actual solution theory\, yielding well-posedness of the equation given th is model as input.\n(Based on joint works with Felix Otto\, Rhys Steele an d Markus Tempelmayr).\n\nThe talk is in room 004 on ground floor of SISSA\ , via Bonomean 265. Zoom access is also provided.\n LOCATION:https://researchseminars.org/talk/PSMQFT/5/ END:VEVENT END:VCALENDAR