The idea of 'bridge' and its unifying role | Olivia Caramello

The idea of 'bridge' and its unifying role | Olivia Caramello | TEDxLakeComo

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Күн бұрын

Knowledge is not made of isolated watertight compartments. Today, the most innovative ideas originate from the contamination between different fields. In the 60s, the great mathematician Alexander Grothendieck introduced the fundamental notion of topos. Toposes can be effectively used as ‘bridges’ for relating different mathematical theories to each other and studying them from a multiplicity of points of view. Thanks to the power of abstraction, seemingly distant theories and concepts can be related, originating new perspectives and unprecedented solutions. Olivia Caramello explains us the general idea of a ‘bridge object’, as it has been inspired by her work in topos theory.
At the age of 19, she graduates in Mathematics and achieves to get her Piano Diploma. A few years later Olivia obtained her Ph.D. in Mathematics at Trinity College in Cambridge. She has worked at prestigious institutions such as the University of Cambridge, the “Scuola Normale di Pisa”, the Max Planck Institute for Mathematics in Bonn, the University of “Paris 7” and the “Institut des Hautes Études Scientifiques”. She is the author of numerous research articles and has held more the one hundred International seminars. She won the position "Rita Levi Montalcini" - a program funded by MIUR to encourage the return of Italian researchers abroad - and has chosen the University of Insubria as her headquarters. This talk was given at a TEDx event using the TED conference format but independently organized by a local community. Learn more at www.ted.com/tedx

Пікірлер: 8

@pairadeau 5 жыл бұрын

Olivia Caramello is a brilliant mathematician. I hope she continues to bless the community with her innovative ideas and results and I encourage everyone with a passing interest in anything scientific to investigate her work on their own time and at their own pace. It is marvelous work.

@michaelmilbocker4548 4 жыл бұрын

Sheaves encode exactly the data needed to pass between the local (CFT) and global (AdS). Consider any continuous map of topological spaces that determines a sheaf of fractal sets. Let f : Y → X be a continuous map. We define a sheaf Γ(Y/X) on X by setting Γ(Y/X)(U) equal to the sections U → Y, that is, Γ(Y/X)(U) is the fractal set of all continuous functions s : U → Y such that f ∘ s = idU. This sheaf is called the sheaf of chaotic sections of f, and it is especially important when f is the projection of a fiber bundle onto its base fractal space.

@emlmm88 4 жыл бұрын

You mean when f is a bundle map - not necessarily a projection unless the bundle is trivial.

@BlueSoulTiger 4 жыл бұрын

A bold attempt at explaining a powerful and abstract concept. The test of any thinker is the capacity to successfully explain the essence of their ideas in simpler (though not too simple) terms. However I felt that a more inductive approach, working from the concrete to the general - rather than vice versa (the talk started with generalisations before moving to specific examples) - and that using even more specific examples, more concrete, less abstract, language would have been more engaging for a non-professional audience. Beyond me of course: But perhaps not beyond the talented Prof. Dr. Caramello.