BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Eva Miranda & Daniel Peralta-Salas (UPC Barcelona & ICMAT Madrid ( Spain)) DTSTART:20210408T140000Z DTEND:20210408T150000Z DTSTAMP:20260423T023021Z UID:DinAmicI/20 DESCRIPTION:Title: Looking at Euler flows through a contact mirror: Universality and Turing completeness\nby Eva Miranda & Daniel Peralta-Salas (UPC Barcelona & ICMAT Madrid (Spain)) as part of DinAmicI: Another Internet Seminar\n\n\nA bstract\nThe dynamics of an inviscid and incompressible fluid flow on a Ri emannian manifold is governed by the Euler equations. Recently\, Tao launc hed a programme to address the global existence problem for the Euler and Navier Stokes equations based on the concept of universality. Inspired by this proposal\, we show that the stationary Euler equations exhibit severa l universality features\, In the sense that\, any non-autonomous flow on a compact manifold can be extended to a smooth stationary solution of the E uler equations on some Riemannian manifold of possibly higher dimension. \ nThese results can be viewed as lending support to the intuition that solu tions to the Euler equations can be extremely complicated in nature.\nA ke y point in the proof is looking at the h-principle in contact geometry thr ough a contact mirror\, unveiled by Sullivan\, Etnyre and Ghrist more than two decades ago.\n\nWe end up this talk addressing an apparently differen t question: What kind of physics might be non-computational? Using the for mer universality result\, we can establish the Turing completeness of the steady Euler flows\, i.e.\, there exist solutions that encode a universal Turing machine and\, in particular\, these solutions have undecidable tra jectories.. But\, in view of the increase of dimension yielded by our proo f. The question is can this be done in dimension 3? We will prove the exis tence of Turing complete fluid\nflows on a 3-dimensional geometric domain. Our novel strategy uses the computational power of symbolic dynamics and the contact mirror again.\n\nThis talk is based on joint work with Robert Cardona and Fran Presas ( arXiv:1911.01963 and arXiv:2012.12828 )\n LOCATION:https://researchseminars.org/talk/DinAmicI/20/ END:VEVENT END:VCALENDAR