I am in Paris since last Wednesday attending a conference in honor of Alain Connes. The conference started last Thursday at IHES by a talk by Michael Atiyah on “radical new thoughts on the foundations of physics”. Atiyah has been proposing for a couple of years that perhaps one should abandon the idea of predicting the future using the formalism of differential equations and initial value problems. Somehow our short term memory of the past should play a role in predictions. This means that instead of a usual differential equation or PDE one should use a “delayed differential equation”. Other talks in the first day were by Manin (“cohomomorphisms and operads”); Katia Consani (“vanishing cycles: an adelic analogue”), Matilde Marcolli (“how noncommutative geometry looks at number theory”).
The first talk on Friday was by Erling Stormer who gave a survey of entropy for operator algebras which was introduced in the seventies by Connes and Stormer in order to classify shifts of the II_1 hyperfinite factor. The second talk was by Alain who explained his approach to the standard model. He showed in particular how the work on renormalization and motivic Galois theory fits with the understanding of the extremely complex Lagrangian of gravity coupled with matter as unveiling the fine texture of space-time using the spectral action principle. He described the physics part of his forthcoming book (634 pages, joint with Matilde Marcolli) which is divided between number theory and physics half and half. At the end of the talk he explained the link between the two parts of the book based on the analogy between the electroweak phase transition in the standard model and the phase transitions which play a crucial role in the quantum statistical mechanics models involved in the approach to RH. In particular he proposed to extend the symmetry breaking to the full gravitational sector so that geometry appears only at low temperature as an emerging phenomenon.
The last talk on Friday was by Don Zagier who talked on `quantum modular forms’.
Friday ended with a wonderful piano concert (Chopin) and poetry session, with pianist Lydie Solomon at the piano and the poetess Nicole Barriere who read 20th century poetry and one of her poems.
I shall report soon on the lectures of this week.