Higher Structures Emerging from Renormalisation - partially postponed

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

Update:
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
10:00 — 10:15
Break
10:15 — 11:00
11:00 — 11:15
Break
11:15 — 12:00
Klaus Fredenhagen (U Hamburg)
Renormalization and C*-algebras
12:00 — 13:15
Lunch Break
13:15 — 14:00
Bruno Vallette (Sorbonne U, Paris)
Operadic renormalisation group
14:00 — 14:15
Break
14:15 — 15:00
Loic Foissy (U of Littoral Côte d’Opale, Dunkerque)
Cointeracting bialgebras
15:00 — 15:30
Break
15:30 — 16:15
Oct. 13, 2020
09:15 — 10:00
Alexander Schmeding (U of Bergen)
Lie groups of Hopf algebra characters
10:00 — 10:15
Break
10:15 — 11:00
11:00 — 11:15
Break
12:00 — 13:15
Lunch Break
13:15 — 14:00
Dominique Manchon (U Clerment Auvergne)
Families of algebraic structures
14:00 — 14:15
Break
14:15 — 15:00
15:00 — 15:30
Break
15:30 — 16:15
16:15 — 16:30
Break
16:30 — 17:15
Oct. 14, 2020
09:15 — 10:00
10:00 — 10:15
Break
11:00 — 11:15
Break
11:15 — 12:00
12:00 — 13:15
Lunch Break
13:15 — 14:00
Enrico Russo (Sorbonne U, Paris)
Renormalisation through WSD equations
14:00 — 14:15
Break
14:15 — 15:00
15:00 — 15:30
Break
15:30 — 16:15
16:15 — 16:30
Break
16:30 — 17:15
Topical Discussion
Oct. 15, 2020
10:00 — 10:15
Break
10:15 — 11:00
Ajay Chandra (Imperial College, London)
Regularity and Coherence of Modelled Distributions
11:00 — 11:15
Break
12:00 — 13:15
Lunch Break
13:15 — 14:00
Antoine Hocquet (TU Berlin)
Monoid-valued Sewing Lemmata and applications
14:00 — 14:15
Break
14:15 — 15:00
15:00 — 15:30
Break
15:30 — 16:15
16:15 — 16:30
Break
16:30 — 17:15
Oct. 16, 2020
09:15 — 10:00
Beatrice de Tiliere (U Paris-Dauphine)
Elliptic dimers and genus 1 Harnack curves
10:00 — 10:15
Break
11:00 — 11:15
Break
11:15 — 12:00
Michał Wrochna (U of Cergy-Pontoise)
Why do we need de Sitter space?
12:00 — 13:15
Lunch Break
13:15 — 14:00
Nicolas Gilliers (NTNU, Trondheim)
Shuffle algebras in operator-valued probability theory.
14:00 — 14:15
Break
14:15 — 15:00
15:00 — 15:30
Break
15:30 — 16:15
16:15 — 16:30
Break
16:30 — 17:15

Organizers

Name Affiliation
Pierre Clavier University of Upper Alsace
Kurusch Ebrahimi-Fard Norwegian University for Science and Technology
Peter K. Friz Technical University Berlin
Harald Grosse University of Vienna
Dominique Manchon Clerment Auvergne University
Sylvie Paycha University of Potsdam
Sylke Pfeiffer University of Potsdam

Attendees

Name Affiliation
Dorothea Bahns University of Göttingen
Ismaël Bailleul Université de Rennes 1
Florian Bechtold Sorbonne University
Carlo Bellingeri Technical University Berlin
Marc Bellon Sorbonne University
Nils Berglund University of Orléans
Emilien Bodiot Sorbonne University
Olivier Bouillot Gustave Eiffel University
Youness Boutaib RWTH Aachen
Johannes Branahl University of Münster
Christian Brouder Sorbonne University
Yvain Bruned University of Edinburgh
Damien Calaque University of Montpellier
Diego de Jesus Caudillo Amador Norwegian University for Science and Technology
Adrián Celestino Rodriguez Norwegian University for Science and Technology
Ajay Chandra Imperial College London
Ilya Chevyrev University of Edinburgh
Antoine Dahlqvist University of Sussex
Viet Dang Nguyen University of Lyon
Claudio Dappiaggi University of Pavia
Nicolas Delporte Université Paris-Saclay
Beatrice de Tiliere Université Paris-Dauphine
Joscha Diehl University of Greifswald
Nicolò Drago University of Würzburg
Gerald Dunne University of Connecticut
Frederic Fauvet University of Strasbourg
Loic Foissy University of Littoral Côte d’Opale
Alessandra Frabetti University of Lyon
Klaus Fredenhagen University of Hamburg
Stefan Fredenhagen University of Vienna
Alfonso Garmendia University of Potsdam
Nicolas Gilliers Norwegian University for Science and Technology
Lisa Glaser University of Vienna
Li Guo Rutgers University
Georges Habib Lebanese University
Mahdi J. Hasan Al-Kaabi Mustansiriyah University
Estanislao Herscovich Université Grenoble Alpes
Antoine Hocquet Technical University Berlin
Joachim Kock University Autonoma de Barcelona
Dirk Kreimer Humboldt University
Antti Kupiainen University of Helsinki
Franz Lehner Technische Universität Graz
Malte Leimbach Freie Universität Berlin
Fei Li Peking University
Ihsane Malass University of Potsdam
Claudia Malvenuto Sapienza – Università di Roma
Cecile Mammez University of Lille
Christoph Minz University of York
Antoine Mouzard Université de Rennes 1
Mohamed Ouerfelli Centre d'Energie Atomique Saclay
Frederic Patras Université Côte d'Azur
Ludwig Rahm Norwegian University for Science and Technology
Kasia Rejzner University of York
Paolo Rinaldi University of Pavia
Vincent Rivasseau Université Paris Sud
Victor Roca Lucio Université Sorbonne Paris Nord
Claude Roger University of Lyon
Enrico Russo Sorbonne University
Alexander Schmeding University of Bergen
Leila Schneps CNRS
Harprit Singh Imperial College London
Thomas Strobl University of Lyon
Aniruddha Talele Rutgers University
Nikolas Tapia Technical University Berlin
Josef Teichmann ETH Zürich
Juraj Tekel Comenius University
Bruno Vallette Sorbonne University
Yannic Vargas University of Potsdam
Xiaoyan Wang Rutgers University
Michał Wrochna CY Cergy Paris Université
Raimar Wulkenhaar University of Münster
Lorenzo Zambotti Sorbonne University
Bin Zhang Sichuan University
Preview of Lorenzo Zambotti - A Microlocal Approach to Renormalization in Stochastic PDEs
Lorenzo Zambotti (Sorbonne U, Paris): A Microlocal Approach to Renormalization in Stochastic PDEs
Oct. 12, 2020 10:15 — 11:00
Preview of Klaus Fredenhagen - Renormalization and C*-algebras
Klaus Fredenhagen (U Hamburg): Renormalization and C*-algebras
Oct. 12, 2020 11:15 — 12:00
Preview of Bruno Vallette - Operadic renormalisation group
Bruno Vallette (Sorbonne U, Paris): Operadic renormalisation group
Oct. 12, 2020 13:15 — 14:00
Preview of Loic Foissy - Cointeracting bialgebras
Loic Foissy (U of Littoral Côte d’Opale, Dunkerque): Cointeracting bialgebras
Oct. 12, 2020 14:15 — 15:00
Preview of Loic Foissy - Cointeracting bialgebras
Loic Foissy (U of Littoral Côte d’Opale, Dunkerque): Cointeracting bialgebras
Oct. 12, 2020 14:15 — 15:00
Preview of Dirk Kreimer - Renormalization, Categories and Self-similarity
Dirk Kreimer (HU Berlin): Renormalization, Categories and Self-similarity
Oct. 12, 2020 15:30 — 16:15
Preview of Nicolas Delporte - Three roads from tensors models to continuous geometry
Vincent Rivasseau (U Paris Sud): Three roads from tensors models to continuous geometry
Oct. 13, 2020 10:15 — 11:00
Preview of Joscha Diehl - Tropical quasisymmetric functions
Joscha Diehl (U Greifswald): Tropical quasisymmetric functions
Oct. 13, 2020 14:15 — 15:00
Preview of Ajay Chandra - Regularity and Coherence of Modelled Distributions
Ajay Chandra (Imperial College, London): Regularity and Coherence of Modelled Distributions
Oct. 15, 2020 10:15 — 11:00
Preview of Alessandra Frabetti - Transport maps as direct connections on groupoids
Alessandra Frabetti (U Lyon): Transport maps as direct connections on groupoids
Oct. 15, 2020 14:15 — 15:00
Preview of Ismaël Bailleul - Paracontrolled calculus and regularity structures
Ismaël Bailleul (U Rennes 1): Paracontrolled calculus and regularity structures
Oct. 15, 2020 15:30 — 16:15
Preview of eatrice de Tiliere - Elliptic dimers and genus 1 Harnack curvesde
Beatrice de Tiliere (U Paris-Dauphine): Elliptic dimers and genus 1 Harnack curves
Oct. 16, 2020 09:15 — 10:00
At a glance
Type:
Online Workshop
When:
Oct. 12, 2020 — Oct. 16, 2020
Where:
ESI Boltzmann Lecture Hall
Organizer(s):
Pierre Clavier (U of Haut-Alsace)
Kurusch Ebrahimi-Fard (NTNU, Trondheim)
Peter K. Friz (TU Berlin)
Harald Grosse (U of Vienna)
Dominique Manchon (U Clerment Auvergne)
Sylvie Paycha (U of Potsdam)
Sylke Pfeiffer (U of Potsdam)
More:
Website