Journée thématique autour de la renormalisation

lundi 12 juin 2023, 11:00 → 17:00 Europe/Paris

Amphi Curie (école polytechnique)

Anne-Sophie de Suzzoni (école polytechnique)

 

 

 

 

 

 

 

 

Les journées thématiques communes aux laboratoires CMAP CPHT  et CMLS de l'école polytechnique sont des journées de conférences visant un public large de mathématicien-ne-s et de physicien-ne-s. Elles sont ouvertes à tous et toutes.

 

Le thème de la journée du 12 juin est celui de la renormalisation. Nous explorerons ce thème sous différents aspects, notamment à travers le spectre des équations aux dérivées partielles stochastique, de la théorie des champs, et du calcul des variations. .

 

Orateurs :

 

Nils Berglund (université d'Orléans, institut Denis Poisson)

Jonas Lampart (Université de Bourgogne, laboratoire ICB)

Slava Rychkov (IHES)

 

L'inscription est gratuite mais obligatoire pour des raisons logistiques.

 

Accès accueil en voiture et par transport copie.pdf

Curie + honneur.pdf

11:00 → 12:00 Nils Berglund : Renormalisation of static and dynamic Phi^4_d models

The static Phi^4 model on the d-dimensional torus is a well-known toy
model in Euclidean quantum field theory. It is well-posed for d = 1,
and its renormalisation is well-understood for d = 2 and d = 3, thanks
to works by Glimm, Jaffe, and many others. In the dynamic case, the
model becomes a stochastic PDE, motivated by the idea of stochastic
quantization. It is well-posed for d = 1. A proof of existence of
solutions to a renormalised version for d = 2 has been obtained by
Da Prato and Debussche in 2003, while the case d = 3 was first solved
by Martin Hairer in 2014, using his theory of regularity structures.
I will provide an overview of these results, focusing on algebraic
techniques of the proofs, and briefly address more general recent
results on renormalisation of singular SPDEs.

The talk is partly based on the book
https://ems.press/books/elm/232

12:00 → 13:30 Déjeuner

13:30 → 14:30 Slava Rychkov : Real-space renormalization of lattice models using tensor networks

Critical points of lattice models, such as the 3d Ising model, are conjectured by Kenneth Wilson in 1970’s to correspond to fixed points of renormalization group transformations. I will discuss the status of this conjecture, a novel class of renormalization group transformations using the language of tensor networks, a few results which were recently obtained using this language for the high and low-temperature phases of 2d models, and the ongoing progress towards the construction of a nontrivial 2d fixed point. Joint work with Tom Kennedy and Nikolay Ebel.

14:30 → 15:00 Pause Café

15:00 → 16:00 Jonas Lampart : Singular perturbations and renormalisation in non-relativistic quantum field theory

I will explain the relation of ultra-violet renormalisation to the theory of singular perturbations of self-adjoint operators in some examples from non-relativistic quantum field theory.
After introducing the relevant formalism, I will discuss in detail a toy model of particle creation and annihilation at a point source.
I will then outline how the same approach can be extended to more interesting models in which non-relativistic particles interact with a quantum field.
An example is the Bogoliubov-Fröhlich Hamiltonian, modelling the interaction of an impurity in a Bose-Einstein Condensate with the field of Bogoliubov excitations.