Scaling limits, rough paths, quantum field theory: Recent Episodes

Cambridge University

The goal of statistical mechanics is to calculate the properties, at macroscopic length scales, of a system composed of a large number of interacting microscopic subsystems. To formalise having a large ratio between largest and the smallest length scales, limits such as infinite volume limits, hydrodynamic limits and scaling limits are studied. These limits are random fields or, in cases where there is dynamics, solutions of nonlinear partial differential equations driven by white noise. Such limits can have symmetries that are not present before taking the limit; for example infinite volume limits may be translation invariant and scaling limits by construction are scale invariant. Increased symmetry leads to very special, beautiful, objects such as euclidean quantum field theories and specific partial differential equations driven by white noise. Then statistical mechanical models can be classified into universality classes characterised by these limits. We think of this as a search for far reaching extensions of the central limit theorem and the theory of large deviations. The possible limits are characterised by very few parameters. A new feature of these extensions is that limits have to be expressed in the correct variables because divergences are inherent in limits that have enhanced symmetries. This is the famous problem of renormalisation in quantum field theory. Divergences arise from the volume of non-compact symmetry groups of translations and dilations. Likewise for partial differential equations driven by white noise divergences appear in naive attempts to define the nonlinear terms in the equations. The solutions are too rough to permit ordinary pointwise multiplication. In the last few years, the theory of rough paths, existence, uniqueness and large deviations for singular partial differential equations has been making very rapid progress. Our four month program has been designed to foster a natural alliance with mathematical quantum field theory, specifically the theory of the renormalisation group, continuation in dimension, operator product expansions and conformally invariant quantum field theory. We aim for progress in global existence of solutions of stochastic pde, dynamical critical exponents, equilibrium critical exponents, bosonisation in two dimensions, better and more complete constructions of euclidean quantum fields.

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Gubinelli, M Monday 17th December 2018 - 11:00 to 12:30

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Gess, N Wednesday 28th November 2018 - 15:00 to 16:00

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Gunaratnam, T Wednesday 28th November 2018 - 16:00 to 16:30

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Spohn, H Friday 14th December 2018 - 09:00 to 10:00

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Melbourne, I Friday 14th December 2018 - 13:30 to 14:30

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Giacomin, G Friday 14th December 2018 - 14:30 to 15:30

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Landim, C Friday 14th December 2018 - 10:00 to 11:00

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Shen, H Thursday 13th December 2018 - 14:30 to 15:30

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Flandoli, F Thursday 13th December 2018 - 13:30 to 14:30

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Bernardin, C Thursday 13th December 2018 - 10:00 to 11:00

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Weber, H Thursday 13th December 2018 - 09:00 to 10:00

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Xu, W Thursday 13th December 2018 - 11:30 to 12:30

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Kotecky, R Friday 7th December 2018 - 11:00 to 12:30

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Giuliani, A Wednesday 12th December 2018 - 10:00 to 11:00

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Quastel, J Wednesday 12th December 2018 - 11:30 to 12:30

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Osborn, H Wednesday 12th December 2018 - 09:00 to 10:00

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Rhodes, R Tuesday 11th December 2018 - 14:30 to 15:30

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Fyodorov, Y Tuesday 11th December 2018 - 11:30 to 12:30

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Le Doussal, P Tuesday 11th December 2018 - 10:00 to 11:00

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Quastel, J Tuesday 11th December 2018 - 09:00 to 10:00

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Hairer, M Monday 10th December 2018 - 10:00 to 11:00

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Garban, C Monday 10th December 2018 - 14:30 to 15:30

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Corwin, I Monday 10th December 2018 - 16:00 to 17:00

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Schlein, B Monday 10th December 2018 - 11:30 to 12:30

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Souganidis, P Monday 10th December 2018 - 13:30 to 14:30

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Chevyrev, I Friday 23rd November 2018 - 11:00 to 12:30

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Gubinelli, M Monday 19th November 2018 - 11:00 to 12:30

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Mitter, P Friday 16th November 2018 - 11:00 to 12:30

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Brydges, D Friday 9th November 2018 - 11:00 to 12:30

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Mitter, P Wednesday 14th November 2018 - 15:00 to 16:30

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Mitter, P Monday 12th November 2018 - 11:00 to 12:30

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Altman, H Wednesday 7th November 2018 - 16:00 to 16:30

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Hilger, S Wednesday 7th November 2018 - 15:30 to 16:00

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Moinat, A Wednesday 7th November 2018 - 15:00 to 15:30

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Jona-Lasinio, G Monday 5th November 2018 - 10:00 to 11:30

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Jona-Lasinio, G Friday 2nd November 2018 - 11:00 to 12:30

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Jara, M Thursday 1st November 2018 - 11:00 to 12:30

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Jara, M Monday 29th October 2018 - 11:00 to 12:30

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Disertori, M Friday 26th October 2018 - 13:30 to 14:30

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Vignes-Tourneret, F Friday 26th October 2018 - 10:00 to 11:00

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Imbrie, J Friday 26th October 2018 - 14:30 to 15:30

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Bruned, Y Friday 26th October 2018 - 11:30 to 12:30

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Bodineau, T Friday 26th October 2018 - 09:00 to 10:00

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Duplantier, B Thursday 25th October 2018 - 15:00 to 16:00

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Hofmanova, M Thursday 25th October 2018 - 14:00 to 15:00

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Unterberger, J Thursday 25th October 2018 - 10:00 to 11:00

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Franco Flandoli Thursday 25th October 2018 - 11:30 to 12:30

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Chandra, A Thursday 25th October 2018 - 09:00 to 10:00

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Henn, H Tuesday 23rd October 2018 - 14:00 to 15:00

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Hairer, M Wednesday 24th October 2018 - 11:30 to 12:30

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Hollands, S Wednesday 24th October 2018 - 09:00 to 10:00

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Rejzner, K Wednesday 24th October 2018 - 10:00 to 11:00

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Rychkov, S Tuesday 23rd October 2018 - 11:30 to 12:30

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Lohmann, M Tuesday 23rd October 2018 - 15:00 to 16:00

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Porta, M Tuesday 23rd October 2018 - 10:00 to 11:00

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Da Prato, G Tuesday 23rd October 2018 - 09:00 to 10:00

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Gonçalves, P Monday 22nd October 2018 - 14:30 to 15:30

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Salmhofer, M Monday 22nd October 2018 - 16:00 to 17:00

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Bach, V Monday 22nd October 2018 - 11:00 to 12:00

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Abdesselam, A Monday 22nd October 2018 - 13:30 to 14:30

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Jona-Lasinio, G Monday 22nd October 2018 - 09:30 to 10:30

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Giuliani, A Friday 19th October 2018 - 11:00 to 12:30

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Giuliani, A Wednesday 17th October 2018 - 15:00 to 16:30

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Giuliani, A Monday 15th October 2018 - 11:00 to 12:30

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Toninelli, F Friday 12th October 2018 - 11:00 to 12:30

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Toninelli, F Wednesday 10th October 2018 - 15:30 to 17:00

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Weber, H Friday 5th October 2018 - 11:00 to 12:30

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Hairer, M Friday 28th September 2018 - 16:00 to 17:00

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Disertori, M Wednesday 19th September 2018 - 15:30 to 16:30

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Disertori, M Wednesday 12th September 2018 - 15:00 to 16:30

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Gubinelli, M Friday 7th September 2018 - 13:30 to 14:30

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Kopper, C Thursday 6th September 2018 - 16:00 to 17:00

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Slade, G Friday 7th September 2018 - 11:30 to 12:30

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Bauerschmidt, R Friday 7th September 2018 - 09:00 to 10:00

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Slade, G Friday 7th September 2018 - 10:00 to 11:00

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Zambotti, L Thursday 6th September 2018 - 14:30 to 15:30

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Slade, G Thursday 6th September 2018 - 11:30 to 12:30

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Otto, F Thursday 6th September 2018 - 13:30 to 14:30

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Slade, G Thursday 6th September 2018 - 09:00 to 10:00

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Perkowski, N Thursday 6th September 2018 - 10:00 to 11:00

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Knoerrer, H Wednesday 5th September 2018 - 11:30 to 12:30

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Zambotti, L Wednesday 5th September 2018 - 10:00 to 11:00

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Otto, F Wednesday 5th September 2018 - 09:00 to 10:00

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Rychkov, S Tuesday 4th September 2018 - 16:00 to 17:00

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Mastropietro, V Tuesday 4th September 2018 - 13:30 to 14:30

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Kupiainen, A Tuesday 4th September 2018 - 11:30 to 12:30

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Kupiainen, A Tuesday 4th September 2018 - 14:30 to 15:30

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Zambotti, L Tuesday 4th September 2018 - 10:00 to 11:00

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Otto, F Tuesday 4th September 2018 - 09:00 to 10:00

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Otto, F Monday 3rd September 2018 - 16:00 to 17:00

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Zambotti, L Monday 3rd September 2018 - 14:30 to 15:30

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Hairer, M Monday 3rd September 2018 - 13:30 to 14:30

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Kupiainen, A Monday 3rd September 2018 - 11:30 to 12:30

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Kupiainen, A Monday 3rd September 2018 - 10:00 to 11:00