Frontiers Lectuer: Alain Connes

Last night (18th April) I attended a talk given by Prof. Alain Connes as part of the The Learned Society of Wales Frontiers lectrures. The talk was entitled “The spectral point of view on geometry and physics”.

Connes

The talk was very interesting and not too technical. Prof. Connes outlined his philosophy that the physical word should be described by spectral data. This idea really leads to the notion of noncommutative geometry, something Prof. Connes is well-know for.

Connes philosophy comes from many facts of physics. For example, our knowledge of the shape of the Universe comes from spectra data, the red shift and the CMBR. The meter is defined in a natural way in terms of the wavelength of the krypton-86 emission.

The key idea

The question that Connes really tackled was can we understand geometry spectrally? Connes was motivated by the Atiyah-Singer index theorem, which gives topological data about a space from analytical data about operators on that space.

The fundamental idea is that one can restate Riemannian geometry in terms of the spectra of the Dirac operator on that geometry. The topological (smooth) structure of the manifold is recovered from the algebra of (smooth) functions and the metric structure from the spectra of the Dirac operator.

One can then understand a smooth manifold with a Riemannian metric in terms of an algebra of functions and an operator acting on them.

Note that we do not need the notion of points in this spectal description. In fact, this reformulation of Rienamnnian geometry allows one to define metrics on non-commutative spaces, which are really just algebras.

Applications

One of the main hopes of Connes reformulation of Riemannian geometry is that, via non-commutative geometry, one can classically unite the standard model of particle physics with general relativity in a geometric way. In doing so, it may be possible to construct a unified theory, but Connes is not at that stage.

As it stands, Connes theory does not quite match the standard model and there is also the problem of Lorentzian signature metrics. Not having positve definite metrics almost always makes details of the mathematics tricky.

This should not distract from the fact that Connes is a pioneer of non-commutative geometry and mathematically his work is very important.

The talk itself

Connes is a good and entertaining speaker. If you get chance to listen to him, you should take it.

Do medical students need physics?

Well, Professor Sir Peter Knight, President of the Institute of Physics say they do…

Physics has transformed medicine and, as this transformation is surely set to continue and accelerate, medical schools should consider restoring the requirement for applicants to hold A level or equivalent qualifications in physics

Professor Sir Peter Knight

As I see it there are at least two areas that knowing a little physics can go a long way

  • Medical devices
  • Biomechanics

Not that we need all medical doctors to be experts in the above, but having some grasp of the physics behind the tools they use and the basic phsyics of the body would, in my opinion, be a good thing.

Slightly wider than just medical students, I am often suprised by just how little mathematics and physics typical biology students known.

On the 18th April five articles were publiched in the Lancet that discuss the historical links between physics and medicine. This I think is a shame. That said, I have no great knowledge of biology!

This reminds me of the idea of evidence based medicine. Which is basically using the ethos of the scientific method to make informed evidenced based treatments. My experience of medicine is a mix of dogma, experience and informed guesses. Anyway, I think a post on evidence based medicine is outside of my remit at the moment.

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