Higher Structures Emerging from Renormalisation

The meeting which aims at offering a place to create new as well as enhance already existing interactions between different aspects of renormalisation in mathematics and physics, comprises

  • a research school (postponed to 2021) with some four introductory 4hrs mini-courses by I. Chevyrev (U. Oxford, UK), F. Patras (CNRS, U. Nice, France), K. Rejzner (U. York, UK) and L. Zambotti (U. Paris, France)
  • an international research workshop (October 12th to October 16th 2020)

with talks by Y. Bruned (U. Edinburgh), A. Cattaneo (ETH Zürich), A. Chandra (Imperial College London), K. Fredenhagen (U. Hamburg), D. Kreimer (Humboldt U., Bverlin) and R. Wulkenhaar (U. Münster) among many other speakers.

Titles and abstracts collection of the online-workshop (pdf)

Slides of the talks of the online workshop:
Monday, October 12, 2020
Loic Foissy, Klaus Fredenhagen, Dirk Kreimer, Leila Schneps, Bruno Vallette, Lorenzo Zambotti

Tuesday, October 13, 2020
Joscha Diehl, Li Guo, Franz Lehner, Dominique Manchon, Kasia Rejzner, Vincent Rivasseau, Alexander Schmeding

Wednesday, October 14, 2020
Marc Bellon, Damien Calaque, Gerald Dunne, Claudia Malvenuto, Enrico Russo, Raimar Wulkenhaar

Thursday, October 15, 2020
Ismael Bailleul, Yvain Bruned, Ajay Chandra, Alessandra Frabetti, Antoine Mouzard, Nikolas Tapia

Friday, October 16, 2020
Beatrice de Tiliere, Nicolas Gilliers, Antti Kupiainen, Viet Dank Nguyen, Josef Teichmann, Yannic Vargas, Michal Wrochna

The Research Workshop will take place online (zoom meeting) October 12th to October 16th 2020 due to Covid-19.
After the online-meeting 12-16 October 2020, we  plan to organize a  follow-up  Master class (Research school)
          "Higher Structures Emerging from Renormalisation"
               8-19  November 2021,   ESI, Vienna


Introductory lectures of this Master class will be the following:

Ilya Chevyrev (Univ. of Oxford)

 Hopf and pre-Lie algebras in regularity structures 

Abstract: This mini-course will focus on the algebraic aspects of regularity structures. I will motivate the Hopf algebra appearing in "positive renormalisation" using polynomials and canonical lifts of smooth functions. I will discuss its similarity to the Connes-Kreimer algebra and present a pre-Lie structure obtained from linearising the group product. I will then discuss "negative renormalisation" and the Hopf algebra of sub-forest extractions. Finally, I will show how the two Hopf algebras (co-)interact and discuss the role of pre-Lie algebras in renormalising stochastic PDEs.


Frédéric Patras (Univ. de Nice)

Renormalization à la Wick

Abstract : The mini-course will come back on a classical example of ``finite renormalization'': the theory of Wick polynomials, Wick products and chaos decompositions. The theory will be presented following a Hopf algebraic approach developed recently that parallels the now usual BWH decomposition in pQFT. Its extension to a noncommutative framework will also be explained as well as the connexion of the theory with other phenomena that received recently a renewed attention (quasi-shuffle products in algebra and probability, among others). The course will essentially be based on recent joint works with K. Ebrahimi-Fard, N. Tapia and L. Zambotti.


Kasia Rejzner (Univ. of York)

Renormalization in perturbative algebraic quantum field theory  

Abstract: In this series of lectures I will introduce perturbative algebraic quantum field theory (pAQFT), which is a rigorous framework for constructing interacting QFT models. It uses a formulation of renormalization called Epstein-Glaser renormalization, where no "infinities" are needed and the computation of physical quantities proceeds through the process of extending certain distributions. I will also explain how to incorporate the homological framework of the BV (Batalin-Vilkovisky) formalism into pAQFT and if time permits I will discuss gauge theories.


Lorenzo Zambotti (Univ. Paris VII)

Analytic aspects of regularity structures 

 Abstract: In this mini-course I plan to introduce the main analytic tools of regularity structures. I’ll start from the Reconstruction Theorem and the Schauder estimates in the general setting of germs, and then I’ll explain the definitions of models and modelled distributions with the different operations acting on them. I’ll try to explain how regularity structures are, in multiple ways, a theory of Taylor expansions.
The content of this mini-course will be based on ongoing work with Francesco Caravenna.

Oct. 12, 2020 Oct. 13, 2020 Oct. 14, 2020 Oct. 15, 2020 Oct. 16, 2020
  • Dorothea Bahns (U Göttingen)
  • Ismaël Bailleul (U Rennes 1)
  • Florian Bechtold (Sorbonne U, Paris)
  • Carlo Bellingeri (TU Berlin)
  • Marc Bellon (Sorbonne U, Paris)
  • Nils Berglund (U of Orléans)
  • Emilien Bodiot (Sorbonne U, Paris)
  • Olivier Bouillot (U Gustave Eiffel, Paris)
  • Youness Boutaib (RWTH Aachen)
  • Johannes Branahl (U Münster)
  • Christian Brouder (Sorbonne U, Paris)
  • Yvain Bruned (U Edinburgh)
  • Damien Calaque (U Montpellier)
  • Diego de Jesus Caudillo Amador (NTNU, Trondheim)
  • Adrián Celestino (NTNU, Trondheim)
  • Ajay Chandra (Imperial College, London)
  • Ilya Chevyrev (U Edinburgh)
  • Pierre Clavier (U of Potsdam) — Organizer
  • Antoine Dahlqvist (U Sussex)
  • Viet Dang Nguyen (U Lyon)
  • Claudio Dappiaggi (U Pavia)
  • Nicolas Delporte (U Paris-Saclay)
  • Beatrice de Tiliere (U Paris-Dauphine)
  • Joscha Diehl (U Greifswald)
  • Nicolò Drago (U Würzburg)
  • Gerald Dunne (U of Connecticut)
  • Kurusch Ebrahimi-Fard (NTNU, Trondheim) — Organizer
  • Frederic Fauvet (U Strasbourg)
  • Loic Foissy (U of Littoral Côte d’Opale, Dunkerque)
  • Alessandra Frabetti (U Lyon)
  • Klaus Fredenhagen (U Hamburg)
  • Stefan Fredenhagen (U Vienna)
  • Alfonso Garmendia (U of Potsdam)
  • Nicolas Gilliers (NTNU, Trondheim)
  • Lisa Glaser (U Vienna)
  • Harald Grosse (U Vienna) — Organizer
  • Li Guo (Rutgers U)
  • Georges Habib (Lebanese U, Fanar-Matn)
  • Mahdi J. Hasan Al-Kaabi (Mustansiriyah U)
  • Estanislao Herscovich (U Grenoble Alpes)
  • Antoine Hocquet (TU Berlin)
  • Joachim Kock (U Autonoma, Barcelona)
  • Dirk Kreimer (HU Berlin)
  • Antti Kupiainen (U Helsinki)
  • Franz Lehner (TU Graz)
  • Malte Leimbach (FU Berlin)
  • Fei Li (Peking U)
  • Ihsane Malass (U of Potsdam)
  • Claudia Malvenuto (U Roma 1, Sapienza)
  • Cecile Mammez (U Lille)
  • Dominique Manchon (U of Auvergne) — Organizer
  • Christoph Minz (U of York)
  • Antoine Mouzard (U Rennes 1)
  • Mohamed Ouerfelli (CEA Paris-Saclay)
  • Frederic Patras (U Côte d'Azur, Nice)
  • Sylvie Paycha (U of Potsdam) — Organizer
  • Sylke Pfeiffer (U of Potsdam) — Organizer
  • Ludwig Rahm (NTNU, Trondheim)
  • Kasia Rejzner (U of York)
  • Paolo Rinaldi (U Pavia)
  • Vincent Rivasseau (U Paris Sud)
  • Victor Roca Lucio (Paris 13)
  • Claude Roger (U Lyon)
  • Enrico Russo (Sorbonne U, Paris)
  • Alexander Schmeding (U of Bergen)
  • Leila Schneps (CNRS, Paris)
  • Harprit Singh (Imperial College, London)
  • Thomas Strobl (U Lyon)
  • Aniruddha Talele (Rutgers U)
  • Nikolas Tapia (TU Berlin)
  • Josef Teichmann (ETH Zürich)
  • Juraj Tekel (Comenius U)
  • Bruno Vallette (Sorbonne U, Paris)
  • Yannic Vargas (IVIC, Miranda)
  • Xiaoyan Wang (Rutgers U)
  • Michał Wrochna (U of Cergy-Pontoise)
  • Raimar Wulkenhaar (U Münster)
  • Lorenzo Zambotti (Sorbonne U, Paris)
  • Bin Zhang (Sichuan U)
At a glance
Online Workshop
Oct. 12, 2020 -- Oct. 16, 2020
ESI Boltzmann Lecture Hall
Pierre Clavier (U of Potsdam)
Kurusch Ebrahimi-Fard (NTNU, Trondheim)
Peter K. Friz (TU Berlin)
Harald Grosse (U Vienna)
Dominique Manchon (U of Auvergne)
Sylvie Paycha (U of Potsdam)
Sylke Pfeiffer (U of Potsdam)