Scaling limits, rough paths, quantum field theory

Scaling limits, rough paths, quantum field theory's image
Created: 2018-09-05 13:52
Institution: Isaac Newton Institute for Mathematical Sciences
Description: 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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A PDE construction of the Euclidean Φ43 quantum field theory

   25 views

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

Collection: Scaling limits, rough paths, quantum field theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Mon 29 Oct 2018


A stochastic approach to constructive QFT

   31 views

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

Collection: Scaling limits, rough paths, quantum field theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Mon 24 Sep 2018


A variational approach to Phi^4_3

   19 views

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

Collection: Scaling limits, rough paths, quantum field theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 21 Nov 2018


An abstract framework for a non-perturbative renormalisation

   5 views

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

Collection: Scaling limits, rough paths, quantum field theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 12 Dec 2018


Bessel S(P)DEs : a story of renormalization

   18 views

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

Collection: Scaling limits, rough paths, quantum field theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Thu 8 Nov 2018


Beyond the van Hove time scale

   5 views

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

Collection: Scaling limits, rough paths, quantum field theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 23 Oct 2018


Bogoliubov Excitations of dilute Bose-Einstein Condensates

   6 views

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

Collection: Scaling limits, rough paths, quantum field theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 11 Dec 2018


BV functions in separable Hilbert spaces

   17 views

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

Collection: Scaling limits, rough paths, quantum field theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 24 Oct 2018


CFT and the bootstrap

   17 views

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

Collection: Scaling limits, rough paths, quantum field theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 5 Sep 2018


CLE Nesting and Liouville Quantum Gravity

   8 views

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

Collection: Scaling limits, rough paths, quantum field theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Mon 29 Oct 2018


Constructive Tensor Field Theory through an example

   12 views

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

Collection: Scaling limits, rough paths, quantum field theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Mon 29 Oct 2018


Deterministic homogenization with Levy process limits

   9 views

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

Collection: Scaling limits, rough paths, quantum field theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Fri 14 Dec 2018


Dynamic ASEP

   9 views

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

Collection: Scaling limits, rough paths, quantum field theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 11 Dec 2018


Edge universality in interacting topological insulators

   12 views

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

Collection: Scaling limits, rough paths, quantum field theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 24 Oct 2018


Elliptic stochastic quantisation

   13 views

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

Collection: Scaling limits, rough paths, quantum field theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 18 Dec 2018


Feshbach-Schur RG for the Anderson Model

   8 views

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

Collection: Scaling limits, rough paths, quantum field theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Mon 29 Oct 2018


Functional Integrals for Bose-Fermi Systems

   6 views

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

Collection: Scaling limits, rough paths, quantum field theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 23 Oct 2018


Generalized hydrodynamics and the classical Toda chain

   5 views

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

Collection: Scaling limits, rough paths, quantum field theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Fri 14 Dec 2018


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