Renormalisation in quantum field theory and in stochastic partial differential equations: a gentle introduction and some recent developments
Monday 3rd September 2018 to Friday 7th September 2018
09:00 to 09:50  Registration  
09:50 to 10:00  Welcome from David Abrahams (INI Director)  
10:00 to 11:00 
Antti Kupiainen (University of Helsinki) Introduction to the Renormalisation Group  1
Lecture notes for the course are at:
https://courses.helsinki.fi/sites/default/files/coursematerial/4594153/MathPhys2018final.pdf
We discuss parts of sections 4,6,7,8,9 which are self contained

INI 1  
11:00 to 11:30  Morning Coffee  
11:30 to 12:30 
Antti Kupiainen (University of Helsinki) Introduction to the Renormalisation Group  2 
INI 1  
12:30 to 13:30  Buffet Lunch at INI  
13:30 to 14:30 
Martin Hairer (Imperial College London) Stochastic quantisation of YangMills
Coauthors: Ajay Chandra (Imperial College London), Hao Shen (Columbia University)

INI 1  
14:30 to 15:30 
Lorenzo Zambotti (Université Pierre et Marie Curie Paris) Renormalisation in regularity structures  part 1
This should be a minicourse on the algebraic side of the theory of regularity structures.

INI 1  
15:30 to 16:00  Afternoon Tea  
16:00 to 17:00 
Felix Otto (MaxPlanckInstitut für Mathematik, Leipzig) Regularity structures: Reconstruction and Integration  part 1
This minicourse is coordinated with the one of
Lorenzo Zambotti. The joint goal is to treat the dynamical phi43 model. This
minicourse will provide the basic notions in regularity structures and discuss
reconstruction and integration. It will mostly follow Martin Hairer's 2015
notes "Regularity structures and the dynamical phi43 model''.

INI 1  
17:00 to 18:00  Welcome Wine Reception at INI 
09:00 to 10:00 
Felix Otto (MaxPlanckInstitut für Mathematik, Leipzig) Regularity structures: Reconstruction and Integration  part 2
This minicourse is coordinated with the one of Lorenzo Zambotti. The joint goal is to treat the dynamical phi43 model. This minicourse will provide the basic notions in regularity structures and discuss reconstruction and integration. It will mostly follow Martin Hairer's 2015 notes "Regularity structures and the dynamical phi43 model''.

INI 1  
10:00 to 11:00 
Lorenzo Zambotti (Université Pierre et Marie Curie Paris) Renormalisation in regularity structures  part 2
This should be a minicourse on the algebraic side of the theory of regularity structures.

INI 1  
11:00 to 11:30  Morning Coffee  
11:30 to 12:30 
Antti Kupiainen (University of Helsinki) Introduction to the Renormalisation Group  3 
INI 1  
12:30 to 13:30  Buffet Lunch at INI  
13:30 to 14:30 
Vieri Mastropietro (Università degli Studi di Milano) Universality in solid state physics and Constructive Renormalization Group
I will review some universality results in graphene and Hall insulators obtained by Renormalization Group methods.

INI 1  
14:30 to 15:30 
Antti Kupiainen (University of Helsinki) Introduction to the Renormalisation Group  4 
INI 1  
15:30 to 16:00  Afternoon Tea  
16:00 to 17:00 
Slava Rychkov (IHES); (École Normale Supérieure) CFT and the bootstrap 
INI 1 
09:00 to 10:00 
Felix Otto (MaxPlanckInstitut für Mathematik, Leipzig) Regularity structures: Reconstruction and Integration  part 3
This minicourse is coordinated with the one of
Lorenzo Zambotti. The joint goal is to treat the dynamical phi43 model. This
minicourse will provide the basic notions in regularity structures and discuss
reconstruction and integration. It will mostly follow Martin Hairer's 2015
notes "Regularity structures and the dynamical phi43 model''.

INI 1  
10:00 to 11:00 
Lorenzo Zambotti (Université Pierre et Marie Curie Paris) Renormalisation in regularity structures  part 3
This should be a minicourse on the algebraic side of the theory of regularity structures.

INI 1  
11:00 to 11:30  Morning Coffee  
11:30 to 12:30 
Horst Knoerrer (ETH Zürich) Symmetry breaking in a gas of bosons  an approach using constructive field theory
T.Balaban, J.Feldman, E.Trubowitz and the speaker have the long term goal to rigorously demonstrate symmetry breaking in a gas of weakly interaction bosons hopping on a threedimensional lattice. Technically, to show that the correlation functions decay at a nonintegrable rate when the chemical potential is sufficiently positive, the nonintegrability reflecting the presence of a long range Goldstone boson mediating the inteaction between quasiparticles in the superfluid condensate.
In addition to a report on the status of this program, I will try to describe in more detail the method of block spin transformations that we use to define and control a renormalization group flow.

INI 1  
12:30 to 13:30  Buffet Lunch at INI  
13:30 to 17:00  Free Afternoon  
19:30 to 22:00  Formal Dinner at Gonville & Caius College 
09:00 to 10:00 
Gordon Slade (University of British Columbia) Renormalisation group and critical phenomena  1
The understanding of critical phenomena via the renormalisation group approach is one of the great achievements of theoretical physics during the last half of the previous century. This series of lectures will begin with an introduction to the critical behaviour of the phi^4 lattice spin system and its supersymmetric counterpart (the weakly selfavoiding walk). The lectures will mainly be occupied with an introduction to a rigorous renormalisation group method that has been developed and used to compute critical exponents for these models in the upper critical dimension d=4, and also below the critical dimension for longrange models. The lectures are based on collaborations with David Brydges and Roland Bauerschmidt.

INI 1 
10:00 to 11:00 
Nicolas Perkowski (HumboldtUniversität zu Berlin) Infinitedimensional paracontrolled distributions: the Burgers generator
Regularity structures, paracontrolled distributions and all that provide pathwise, deterministic tools to solve and study singular stochastic PDEs over finitedimensional spaces. From a probabilistic point of view we would also like to understand the associated Kolmogorov backward equations, which can be interpreted as infinitedimensional singular SPDEs. I will discuss on the example of the conservative stochastic Burgers equation how to construct a space of (para) paracontrolled distributions in which the backward equation is well posed. As an application we obtain a martingale formulation and an alternative proof for the wellposedness of "energy solutions", without using the ColeHopf transform. The approach extends to some other singular SPDEs with Gaussian invariant measures and quadratic nonlinearities. This is joint work with Massimiliano Gubinelli.

INI 1 
11:00 to 11:30  Morning Coffee  
11:30 to 12:30 
Gordon Slade (University of British Columbia) Renormalisation group and critical phenomena  2
The understanding of critical phenomena via the renormalisation group approach is one of the great achievements of theoretical physics during the last half of the previous century. This series of lectures will begin with an introduction to the critical behaviour of the phi^4 lattice spin system and its supersymmetric counterpart (the weakly selfavoiding walk). The lectures will mainly be occupied with an introduction to a rigorous renormalisation group method that has been developed and used to compute critical exponents for these models in the upper critical dimension d=4, and also below the critical dimension for longrange models. The lectures are based on collaborations with David Brydges and Roland Bauerschmidt.

INI 1 
12:30 to 13:30  Buffet Lunch at INI  
13:30 to 14:30 
Felix Otto (MaxPlanckInstitut für Mathematik, Leipzig) Regularity structures: Reconstruction and Integration  part 4
This minicourse is coordinated with the one of Lorenzo Zambotti. The joint goal is to treat the dynamical phi43 model. This minicourse will provide the basic notions in regularity structures and discuss reconstruction and integration. It will mostly follow Martin Hairer's 2015 notes "Regularity structures and the dynamical phi43 model''.

INI 1 
14:30 to 15:30 
Lorenzo Zambotti (Université Pierre et Marie Curie Paris) Renormalisation in regularity structures  part 4
This should be a minicourse on the algebraic side of the theory of regularity structures.

INI 1 
15:30 to 16:00  Afternoon Tea  
16:00 to 17:00 
Christoph Kopper (École Polytechnique) The Flow equations of the renormalization group
The Flow equations in Polchinski's setting allow for a simple and transparent proof of perturbative renormalizability, cirumventing auxiliary combinatoric structures.
They also permit to prove properties of perturbative Schwinger functions which are out of reach in other settings. The main problem for a nonperturbative analysis of those equations lies in their combinatoric instability, which is present already at the mean field level.

INI 1 
17:15 to 18:15 
Antti Kupiainen (University of Helsinki) Wilsonian RG for SPDEs (Informal discussion) 
INI 1 
09:00 to 10:00 
Roland Bauerschmidt (University of Cambridge) Spectral gap critical exponent for Glauber dynamics of hierarchical spin models
We develop a renormalisation group approach to deriving the asymptotics of the spectral gap of the generator of Glauber type dynamics of spin systems at and near a critical point. In our approach, we derive a spectral gap inequality, or more generally a BrascampLieb inequality, for the measure recursively in terms of spectral gap or BrascampLieb inequalities for a sequence of renormalised measures. We apply our method to hierarchical versions of the $4$dimensional $n$component $\varphi^4$ model at the critical point and its approach from the high temperature side, and the $2$dimensional SineGordon and the Discrete Gaussian models in the rough phase (KosterlitzThouless phase). For these models, we show that the spectral gap decays polynomially like the spectral gap of the dynamics of a free field (with a logarithmic correction for the $\varphi^4$ model), the scaling limit of these models in equilibrium.
Coauthor: Thierry Bodineau

INI 1 
10:00 to 11:00 
Gordon Slade (University of British Columbia) Renormalisation group and critical phenomena  4
The understanding of critical phenomena via the renormalisation group approach is one of the great achievements of theoretical physics during the last half of the previous century. This series of lectures will begin with an introduction to the critical behaviour of the phi^4 lattice spin system and its supersymmetric counterpart (the weakly selfavoiding walk). The lectures will mainly be occupied with an introduction to a rigorous renormalisation group method that has been developed and used to compute critical exponents for these models in the upper critical dimension d=4, and also below the critical dimension for longrange models. The lectures are based on collaborations with David Brydges and Roland Bauerschmidt.

INI 1 
11:00 to 11:30  Morning Coffee  
11:30 to 12:30 
Gordon Slade (University of British Columbia) Renormalisation group and critical phenomena  3
The understanding of critical phenomena via the renormalisation group approach is one of the great achievements of theoretical physics during the last half of the previous century. This series of lectures will begin with an introduction to the critical behaviour of the phi^4 lattice spin system and its supersymmetric counterpart (the weakly selfavoiding walk). The lectures will mainly be occupied with an introduction to a rigorous renormalisation group method that has been developed and used to compute critical exponents for these models in the upper critical dimension d=4, and also below the critical dimension for longrange models. The lectures are based on collaborations with David Brydges and Roland Bauerschmidt.

INI 1 
12:30 to 13:30  Buffet Lunch at INI  
13:30 to 14:30 
Massimiliano Gubinelli (Universität Bonn) A stochastic approach to constructive QFT
Coauthor: Nikolay Barashkov (University of Bonn) We propose a new existence proof of the Phi^4_{2,3} Euclidean quantum fields in a periodic domain using tools from stochastic analysis, in particular a stochastic control interpretation of Wilson's continuous RG. 
INI 1 