# Scaling limits, rough paths, quantum field theory

Created: | 2018-09-05 13:52 |
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Institution: | Isaac Newton Institute for Mathematical Sciences |

Editors' group: | Members of "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. |

# Media items

This collection contains 94 media items.

### Media items

#### A PDE construction of the Euclidean Φ43 quantum field theory

28 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 scaling limit from Euler to Navier-Stokes equations with random perturbation

17 views

Franco Flandoli

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

**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

35 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

21 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

7 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

7 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

19 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

19 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

11 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

20 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

9 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

#### Freezing Transition in Decaying Burgers Turbulence and Random Matrix Dualities

8 views

Fyodorov, Y

Tuesday 11th December 2018 - 11:30 to 12:30

**Collection**:
Scaling limits, rough paths, quantum field theory

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 12 Dec 2018

#### Functional Integrals for Bose-Fermi Systems

8 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