Workshop on Higher Structures and Operadic Calculus (IRP Higher Homotopical Structures)

Sign in
Workshop
From June 21, 2021
to June 25, 2021

Onsite places will be limited, please, let us know if you intend to participate in person by sending an email to crmactivitats@crm.cat by June 13, 2021. If the number of people exceeds the capacity of the room, we will give priority by date of registration. Confirmation will be sent by June 15, 2021.

Registration deadline 13 / 06 / 2021
SCHEDULE
RECORDINGS

Introduction

Since their introduction 50 years ago, the notions of infinity-algebras (Stasheff), operads (May), model categories (Quillen), and higher categories (Boardman-Vogt) gave rise to powerful tools which made possible the resolution of open problems and prompted revolutions in many domains like algebraic topology (rational homotopy theory, faithful algebraic invariants of the homotopy type of spaces), deformation theory (formality theorems, formal moduli problems), and mathematical physics (quantisation of Poisson manifolds, quantum field theories), to name but a few. This theory of higher structures using operadic calculus is currently under rapid development and there is a need today to provide the community with a modern state of the art; this is the main goal of the present workshop, which will be accessible to a wide audience.​

Workshop’s ​information

Topics
  • Rational homotopy theory, Lie/L-infinity-models, Koszul duality, Maurer-Cartan spaces.
  • Configuration spaces, holonomy algebras, connections, associators, operads in groupoids, (prounipotent) Grothendieck-Teichmüller group.
  • Deformation theory, Maurer-Cartan elements, integration theory (gauge group, pre-Lie calculus, infinity-groupoids), formal moduli spaces.
  • Infinity-operads, formality theorems, Hodge theory (purity).
  • (Infinity-)modular operads, moduli spaces of curves, (profinite) Grothendieck-Teichmüller group.

Further information​

For inquiries please contact the Coordinator

Coordinator

Bruno Vallette  ​Université Sorbonne Paris Nord

Speaker​s

Alexander BERGLUND

Stockholm University

ABSTRACT

Higher structures in rational homotopy theory

Higher structures and operadic calculus are essential tools in modern approaches to rational homotopy theory and its applications. The aim of this lecture series is to give an introduction to rational homotopy theory through the lens of higher structures.

The rational homotopy type of a simply connected space is faithfully modeled by the collection of rational homotopy groups together with its minimal L-infinity algebra structure, or by the rational cohomology ring together with its minimal C-infinity algebra structure. These structures are related to higher order Whitehead products and Massey products, respectively. We will review these models and discuss their relation to the classical Sullivan and Quillen models. Then we will give a tour of the interplay between Koszul duality, formality and coformality, focusing on computational aspects. Finally, we will discuss classical and new results on the rational homotopy theory of classifying spaces for fibrations, highlighting connections to higher structures and operadic calculus.

Damien CALAQUE

Université de Montpellier

ABSTRACT

An operadic view on associators

Associators, introduced by Drinfeld, became a central object in mathematics, with applications ranging from algebraic topology (formality of the little disks operad) to mathematical physics (deformation quantization). The aim of this lecture series is to explain the modern operadic approach to associators, and discuss generalizations of these. We will not discuss much of the homotopical aspects of the story.

Ricardo CAMPOS​​

CNRS, Université de Montpellier

ABSTRACT

Operadic deformation theory

A classical heuristic in deformation theory asserts that the infinitesimal deformations of an algebro-geometric object over a field of characteristic zero are controlled by a differential graded Lie algebra. In the setting of algebras over operads, various questions (e.g. formality) can be considered as deformation theoretic problems. In this case the operadic formalism produces very explicit and computable instances of such deformation Lie algebras in a universal way.

On the other hand, some algebraic problems admit a non-obvious deformation theoretic interpretation. In this lecture series we will introduce and give an overview of the recent developments concerning the use of algebraic operads in deformation theory. 

Geoffroy HOREL

​Université Sorbonne Paris Nord

ABSTRACT

Weight structures and formality

I will discuss various formality results revolving around the idea of weight structure. A weight structure is a naturally occurring graduation on the cohomology groups of certain algebraic objects. If this weight structure can be lifted at the level of chains and if it satisfies a property called purity, then one can deduce formality. Algebraic geometry provides us with interesting weight structures as the cohomology of algebraic varieties tends to have additional structure (like a Hodge structure or a Galois action). Using some homotopy theoretic machinery, one can show that these weight structures can be lifted at the level of chains and obtain interesting formality results.

Marcy ROBERTSON​

University of Melbourne

ABSTRACT

Infinity Modular Operads and the Grothendieck-Teichmüller group 

This three part series will discuss several models for infinity cyclic and modular operads and their applications to (profinite) Grothendieck-Teichmüller groups.

The first two talks in the series will cover basics on cyclic and modular operads and introduce models for their infinity counterparts. We will cover multiple models for infinity cyclic and modular operads, but our primary focus will be on a Segal model introduced in joint work with Hackney and Yau. The third talk will focus on applications and examples of infinity cyclic and modular operads with a focus on the applications to (profinite) Grothendieck-Teichmüller theory.

List of on-line participants

Click to open list
Rizal Afgani Bandung Institute of Technology
Nanna Aamand University of Copenhagen
Javier Aguilar Martín University of Kent
Miguel Barrero Radboud University Nijmegen
Matija Bašic University of Zagreb
Luciana Basualdo Bonatto University of Oxford
Sai Bavisetty University of Illinois at Urbana–Champaign
Clemens Berger Université Côte d’Azur
Alexander Berglund ​Stockholm University
Peter Bonventre Georgetown University
Matt Booth University of Antwerp
James Brotherston University of Sheffield
Mauricio Bustamante University of Cambridge
Federico Cantero Morán Universidad Autónoma de Madrid
Juan Carlos Nuñez Maldonado Universidade Federal de São Carlos
Victor Carmona Universidad de Sevilla
Anish Chedalavada Not provided
Sheng-Fu Chiu Academia Sinica
David Corwin University of California at Berkeley
Pierre-Louis Curien Paris Diderot University – Paris 7
Yoann Dabrowski Claude Bernard University Lyon 1
Apurba Das Indian Institute of Technology Kanpur
Marie-Camille Delarue École normale supérieure – Paris
Sophie d’Espalungue University Lille 1: Sciences and Technologies
Ioannis Dokas National and Kapodistrian University of Athens
Eric Dolores-Cuenca NewSci Labs
Steven Duplij (Stepan Douplii) University of Münster
Patrick Elliott University of Melbourne
David Fernández Bielefeld University
Oskar Frost University of Luxembourg
Andrea Gentili Not provided
David Gepner University of Illinois at Chicago
Andrey Glubokov Not provided
Tao Gong Beijing Normal University
Martin Gonzalez Paris Diderot University – Paris 7
Albin Grataloup University of Montpellier
Peiqi Gu Beijing Normal University
Lorenzo Guerra University Lille 1: Sciences and Technologies
Markus Hausmann Not provided
Lander Hermans University of Antwerp
Eric Hoffbeck University of Paris 13
Tamara Hogan University of Melbourne
Asaf Horev Stockholm University
Samuel Hsu University of Illinois at Urbana–Champaign
Zhen Huan Huazhong University of Science and Technology
Langwen Hui University of Oxford
Najib Idrissi Paris Diderot University – Paris 7
Filippos Ilarion Sytilidis University of Oxford
Ángel Javier Alonso Hernández Universidad Autónoma de Madrid
Eilind Karlsson Technical University of Munich
David Kern University of Angers
Andrei Konovalov Not provided
Julien Korinman Waseda University
Danica Kosanovic University of Paris 13
Manuel Krannich University of Cambridge
Kalin Krishna Indian Institute of Science Education and Research Thiruvananthapuram
Sylvain Lavau Saint Petersburg State University
Ishan Levy Massachusetts Institute of Technology
Yifan Li Beijing Normal University
Yingxin Li Beijing Normal University
Jerry Lodder New Mexico State University
Maxime Lucas University of Paris 13
Roy Magen Columbia University
José Manuel Moreno Universidad de Málaga
Ioannis Markakis Not provided
Udit Mavinkurve Western University (The University of Western Ontario)
Antonio Michele Miti Catholic University of the Sacred Heart
Aleksandar Miladinovic University of Paris 13
Syunji Moriya Osaka Prefecture University
Anita Naolekar Indian Statistical Institute
Sam Nariman Purdue University
Silvère Nédélec Federal University of Rio Grande do Sul
Frank Neumann University of Leicester
Joost Nuiten University of Montpellier
Jovana Obradovic Akademie ved Ceské republiky
Santiago Pineda Montoya Not provided
Christopher Portwood North Carolina State University
Amoolya Prasad University of Manchester
Zihao Qi Not provided
Qingrui Qu Beijing Normal University
Ryan Quinn University of Amsterdam
Ismaïl Razack University of Picardie Jules Verne
Saha Ripan Raiganj University
​Marcy Robertson ​University of Melbourne
Chris Rogers University of Nevada – Reno
Yangyang Ruan Beijing Normal University
Lleonard Rubio y Degrassi University of Verona
Leonid Ryvkin University of Göttingen
Pablo S. Ocal Texas A&M University
Paolo Saracco Université libre de Bruxelles
Daniel Scherl University of Hamburg
Silvan Schwarz Swiss Federal Institute of Technology in Zurich
Axel Siberov University of Luxembourg
Chandan Singh University of Melbourne
Dev Sinha University of Oregon
Grigory Solomadin Lomonosov Moscow State University
Kurt Stoeckl University of Melbourne
Robin Stoll Stockholm University
Vignesh Subramanian University of Copenhagen
Pedro Tamaroff Trinity College Dublin
Julienne Théophile École normale supérieure de Lyon
Yannic Vargas Instituto Venezolano de Investigaciones Científicas
Antonio Viruel Universidad de Málaga
Marco Volpe University of Regensburg
Friedrich Wagemann University of Nantes
Benjamin Walter Middle East Technical University
Ran Wang Beijing Normal University
Ben Ward Bowling Green State University
Zhaoting Wei Texas A
Christoph Weis Not provided
Jordan Williamson Charles University in Prague
Yifan Wu Boston College
Runlei Xiao Université de Nice Sophia Antipolis
Hicham Yamoul University of Hassan 2 of Casablanca
Tomas Zeman Stockholm University
Xu-an Zhao Beijing Normal University
Guodong Zhou East China Normal University
Foling Zou University of Michigan
Pál Zsámboki Alfréd Rényi Institute of Mathematics
*Upadated June 15, 2021

List of on-site participants

Click to open list
Xerxes Arsiwalla Universitat Pompeu Fabra
Joan Bellier-Millès Paul Sabatier University – Toulouse III
Carles Broto Universitat Autònoma de Barcelona – CRM
​Damien Calaque ​Université de Montpellier
Marie Camille de la Rue École normale supérieure – Paris
​Ricardo Campos ​CNRS – Université de Montpellier
Carles Casacuberta Universitat de Barcelona
Joana Cirici Universitat de Barcelona
Emprin Coline École normale supérieure – Paris
Imma Gálvez Carrillo Universitat Politècnica de Catalunya
​Geoffroy Horel ​Université Sorbonne Paris Nord
Javier J. Gutiérrez Universitat de Barcelona
Wilson Javier Forero Baquero Universitat Autònoma de Barcelona
Sadok Kallel University Lille 1
Joachim Kock Universitat Autònoma de Barcelona – CRM
Eugenio Landi Roma Tre University
Guillaume Laplante -Anfossi University of Paris 13
Samuel Lavenir Swiss Federal Institute of Technology in Lausanne
Emma Lepri Sapienza University of Rome
Muriel Livernet Université Paris Diderot-Paris 7
Andrea Marino University of Roma Tor Vergata
David Martínez Universitat de Barcelona
Thibaut Mazuir Institut de mathématiques de Jussieu
Anibal Medina Not provided
Bob Oliver University of Paris 13
Hugo Pourcelot University of Paris 13
Daniel Robert-Nicoud Not provided
Víctor Roca Lucio University of Paris 13
Agustí Roig Universitat Politècnica de Catalunya
Tommaso Rossi University of Roma Tor Vergata
Bashar Saleh Universitat de Barcelona
Paolo Salvatore University of Roma Tor Vergata
Andrew Tonks University of Leicester
Dominik Trnka Masaryk University
Bruno Vallette Université Sorbonne Paris Nord
*Updated June 15, 2021

Lodging information

  • For lodging in the area please click here​
  • For off-campus and family accommodation click here​​​

Acknowledgements

 

For inquiries about the activity please contact the research programs coordinator Ms. Núria Hernández at nhernandez@crm.cat​​