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X-WR-CALDESC:Events for DinAmicI
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DTSTART;TZID=Europe/Rome:20210408T160000
DTEND;TZID=Europe/Rome:20210408T170000
DTSTAMP:20210612T130428
CREATED:20210324T093926Z
LAST-MODIFIED:20210416T205516Z
UID:1865-1617897600-1617901200@www.dinamici.org
SUMMARY:Eva Miranda (Universitat Politècnica de Catalunya) and Daniel Peralta-Salas (Instituto de Ciencias Matemáticas\, Spain)
DESCRIPTION:Speakers: Eva Miranda (Universitat Politècnica de Catalunya)\, Daniel Peralta-Salas (Instituto de Ciencias Matemáticas\, Spain) \nTitle: Looking at Euler flows through a contact mirror: Universality and Turing completeness \nAbstract: The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently\, Tao launched 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 several universality features\, In the sense that\, any non-autonomous flow on a compact manifold can be extended to a smooth stationary solution of the Euler equations on some Riemannian manifold of possibly higher dimension. These results can be viewed as lending support to the intuition that solutions to the Euler equations can be extremely complicated in nature. A key point in the proof is looking at the h-principle in contact geometry through a contact mirror\, unveiled by Sullivan\, Etnyre and Ghrist more than two decades ago. We end up this talk addressing an apparently different question: What kind of physics might be non-computational? Using the former 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 trajectories. But\, in view of the increase of dimension yielded by our proof\, the question is: can this be done in dimension 3? We will prove the existence of Turing complete fluid flows on a 3-dimensional geometric domain. Our novel strategy uses the computational power of symbolic dynamics and the contact mirror again.\nThis talk is based on joint work with Robert Cardona and Fran Presas (arXiv:1911.01963 and arXiv:2012.12828). \nNOTE: The seminar will be streamed live on our YouTube channel then saved there. If you ask questions\, with your video feed on or off\, you agree to the use of your image/spoken words for said purpose.
URL:https://www.dinamici.org/event/eva-miranda-universitat-politecnica-de-catalunya-and-daniel-peralta-salas-instituto-de-ciencias-matematicas-spain/
LOCATION:Seminar is over: watch it on our YouTube channel (link below)
CATEGORIES:DAI Seminar
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DTSTART;TZID=Europe/Rome:20210422T160000
DTEND;TZID=Europe/Rome:20210422T170000
DTSTAMP:20210612T130428
CREATED:20210408T220406Z
LAST-MODIFIED:20210423T081514Z
UID:1888-1619107200-1619110800@www.dinamici.org
SUMMARY:Tanja Schindler (Scuola Normale Superiore\, Italy)
DESCRIPTION:Speaker: Tanja Schindler (Scuola Normale Superiore\, Italy) \nTitle: Almost sure asymptotic behaviour of Birkhoff sums for infinite measure-preserving dynamical systems \nAbstract: We are interested in the limit behaviour of Birkhoff sums over an infinite sigma-finite measure space. If the observable is integrable then — by a classical theorem by Aaronson — there exists no sequence of real numbers such that the Birkhoff sum normed by this sequence converges almost surely to 1. Under strong mixing conditions on the underlying system we prove a generalized strong law of large numbers for integrable observables using a truncated sum adding a suitable number of terms depending on the point of evaluation. For f not integrable we give conditions on f such that the Birkhoff sum normed by a sequence of real numbers converges almost surely to 1. Joint work with Claudio Bonanno. \nNOTE: The seminar will be streamed live on our YouTube channel then saved there. If you ask questions\, with your video feed on or off\, you agree to the use of your image/spoken words for said purpose.
URL:https://www.dinamici.org/event/tanja-schindler-scuola-normale-superiore-italy/
LOCATION:Seminar is over: watch it on our YouTube channel (link below)
CATEGORIES:DAI Seminar
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