Grothendieck-Teichmüller groups, deformation and operads

Programme theme

The main goal of this programme is to bring together the two research communities working on Grothendieck-Teichmüller theory on the one hand, and on operadic deformation theory on the other hand. These themes lie at the forefront of current research in algebra, algebraic and differential geometry, number theory, topology and mathematical physics.

Grothendieck-Teichmüller theory goes back to A. Grothendieck's celebrated Esquisse d'un programme. In 1991, V. Drinfel'd formally introduced two Grothendieck-Teichmüller groups, the former one related to the absolute Galois group and the latter one related to the deformation theory of a certain algebraic structure (braided quasi-Hopf algebra). Introduced in algebraic topology 40 years ago, the notion of operad has enjoyed a renaissance in the 90's under the work of M. Kontsevich in deformation theory. Two proofs of the deformation quantization of Poisson manifolds, one by himself as well as one by D. Tamarkin, led M. Kontsevich to conjecture an action of a Grothendieck-Teichmüller group on such deformation quantizations, thereby drawing a precise relationship between the two themes.

Research in mathematics often alternates breakthroughs and periods of sedimentation of ideas. More than 10 years after those major results, the underlying theories have now been well understood and we can expect new important discoveries. Recently, some results have been proved at the intersection of Grothendieck-Teichmüller groups, deformation theory, operads and multiple zeta values. These fields of research clearly overlap and such a programme should facilitate the cross-fertilization between them.

The main topics of the programme are:

Operads (Koszul duality theory, homotopy algebras, moduli space of curves, Deligne conjecture). A graduate course on operads is being given by Bruno Vallette at the University of Copenhagen.
Deformation quantization (Lie bialgebras, Hopf algebras, Poisson manifolds, Kashiwara-Vergne conjecture, Duflo isomorphism)
Grothendieck-Teichmüller theory (absolute Galois group, GT groups and GT Lie algebras, Drinfel'd associators)
Multiple zeta values (mixed Tate motives, polylogarithms, shuffle algebra, Deligne-Ihara algebra)

The programme will include 4 weekly courses, over the course of a month, on the aforementioned topics. The courses will be mainly addressed to students and to non-specialists and will be organised in order to make them accessible to the UK community. Two workshops are also scheduled to cover more advanced results.

The programme is supported by the Clay Mathematics Institute.

Click here to download the programme's final scientific report

Preprints

Title	Year	Programme
The derived Maurer-Cartan locus Authors: Ezra Getzler Download PDF	2012	GDO	2 March 2017
Geometric higher groupoids and categories Authors: Ezra Getzler Download PDF	2012	GDO	2 March 2017
An A$_\infty$ operad in spineless cacti Authors: Imma Gálvez-Carrillo, L Lombardi, A Tonks Download PDF	2012	GDO	21 October 2016
Untwisting a twisted Calabi-Yau algebra Authors: J Goodman, U Krahmer Download PDF	2012	GDO	21 October 2016
Givental action is homotopy gauge symmetry Authors: Vladimir Dotsenko, S Shadrin, Bruno Vallette Download PDF	2012	GDO	21 October 2016
Equations of tropical varieties Authors: Jeffrey Giansiracusa, Jeffrey Giansiracusa Download PDF	2012	GDO	21 October 2016
Modular invariant of quantum tori Authors: C Castano Bernard, Timothy Gendron Download PDF	2012	GDO	21 October 2016
A$_\infty$-actions and recognition of relative loop spaces Authors: Eduardo Hoefel, Muriel Livernet, J Stasheff Download PDF	2012	GDO	21 October 2016
On the equivalence between Lurie's model and the dendroidal model for infinity-operads Authors: G Heuts, V Hinich, Ieke Moerdijk Download PDF	2012	GDO	21 October 2016
Homology of depth-graded motivic Lie algebras and koszulity Authors: Benjamin Enriquez, Pierre Lochak Download PDF	2012	GDO	21 October 2016
Strong homology, and closed geodesics on manifolds which are elliptic spaces Authors: John Jones, John McCleary Download PDF	2012	GDO	21 October 2016

Workshops

GDOW01

Seminars

Tuesday 15th January 2013
14:00 to 17:00	Sergei Merkulov Stockholm University Grothendieck-Teichmüller groups, graph complexes and deformation quantization (Informal talk)	Room 1

Wednesday 16th January 2013
10:30 to 12:00	Bruno Vallette Université de Nice Sophia Antipolis Operads: definition, examples and first properties	Room 1
14:00 to 15:30	Bruno Vallette Université de Nice Sophia Antipolis Koszul duality theory for algebras	Room 1
16:00 to 17:30	Bruno Vallette Université de Nice Sophia Antipolis Operads: exercise session	Room 1

Thursday 17th January 2013
14:00 to 16:00	Dror Bar-Natan University of Toronto Meta-Groups, Meta-Bicrossed-Products, and the Alexander Polynomial	Room 1

Tuesday 22nd January 2013
14:00 to 15:00	Ieke Moerdijk Radboud Universiteit Nijmegen Dendroidal sets and infinity-operads I	Room 2
15:00 to 16:00	Ieke Moerdijk Radboud Universiteit Nijmegen Dendroidal sets and infinity-operads II	Room 2

Wednesday 23rd January 2013
10:30 to 12:00	Bruno Vallette Université de Nice Sophia Antipolis Koszul duality theory for operads	Room 1
14:00 to 15:30	Bruno Vallette Université de Nice Sophia Antipolis Methods for Koszul duality	Room 1
16:00 to 17:30	Bruno Vallette Université de Nice Sophia Antipolis Operads: exercise session	Room 1

Thursday 24th January 2013
14:00 to 15:00	Pierre Cartier IHES Morita equivalence, Tannakian categories and motivic periods I	Room 1
15:00 to 16:00	Pierre Cartier IHES Morita equivalence, Tannakian categories and motivic periods II	Room 1

Tuesday 29th January 2013
14:00 to 15:00	Ieke Moerdijk Radboud Universiteit Nijmegen Dendroidal sets and infinity-operads III	Room 2
15:00 to 16:00	Ieke Moerdijk Radboud Universiteit Nijmegen Dendroidal sets and infinity-operads IV	Room 2

Wednesday 30th January 2013
10:30 to 12:00	Bruno Vallette Université de Nice Sophia Antipolis Homotopy algebras	Room 1
14:00 to 15:30	Bruno Vallette Université de Nice Sophia Antipolis (Co)homology theories and deformation theory	Room 1
16:00 to 17:30	Bruno Vallette Université de Nice Sophia Antipolis Operads: exercise session	Room 1

Thursday 31st January 2013
14:00 to 15:00	Tree-indexed series, theory and examples I	Room 1
15:00 to 16:00	Tree-indexed series, theory and examples II	Room 1

Friday 1st February 2013
10:00 to 12:00	Informal discussion	Discussion Room

Tuesday 5th February 2013
10:30 to 12:00	John Jones University of Warwick The Hochschild cochain complex, operads, and the Deligne conjecture I	Room 1
14:00 to 15:30	John Jones University of Warwick The Hochschild cochain complex, operads, and the Deligne conjecture II	Room 1
16:00 to 17:30	John Jones University of Warwick Deformation theory: exercise session	Room 1

Wednesday 6th February 2013
10:30 to 12:00	Pierre Lochak Institut de Mathématiques de Jussieu A brief introduction to the etale fundamental group and to the Galois action	Room 1
14:00 to 15:30	Pierre Lochak Institut de Mathématiques de Jussieu Profinite braid groups; first appearance of GT	Room 1
16:00 to 17:30	Pierre Lochak Institut de Mathématiques de Jussieu Special Topic: Belyi Theorem and dessins d'enfants	Room 1

Thursday 7th February 2013
14:00 to 15:00	Hypercommutative algebras, Batalin-Vilkovisky algebras, and Givental group I	Room 1
15:00 to 16:00	Hypercommutative algebras, Batalin-Vilkovisky algebras, and Givental group II	Room 1

Friday 8th February 2013
10:30 to 12:00	Ieke Moerdijk Radboud Universiteit Nijmegen Dendroidal sets and infinity-operads III	Room 1

Tuesday 12th February 2013
10:30 to 12:00	Damien Calaque ETH Zürich Formality, obstructions to formality, and a key argument in the proof of the formality conjecture I	Room 1
14:00 to 15:30	Bruno Vallette Université de Nice Sophia Antipolis Formality, obstructions to formality, and a key argument in the proof of the formality conjecture II	Room 1
16:00 to 17:30	Damien Calaque ETH Zürich Deformation theory: exercise session	Room 1

Wednesday 13th February 2013
10:30 to 12:00	Pierre Lochak Institut de Mathématiques de Jussieu Deforming braided categories and a useful dictionary	Room 1
14:00 to 15:30	Leila Schneps Institut de Mathématiques de Jussieu Infinitesimal braid and the Lie algebra of (the prounipotent version of) GT	Room 1
16:00 to 17:30	Pierre Lochak Institut de Mathématiques de Jussieu Special Topic: Associator relations satisfy double shuffle (H. Furusho)	Room 1

Thursday 14th February 2013
14:00 to 16:00	Giovanni Felder ETH Zürich The classical master equation	Room 1

Tuesday 19th February 2013
10:30 to 12:00	John Jones University of Warwick Etingof - Kazhdan quantization of Lie bialgebras I	Room 1
14:00 to 15:30	John Jones University of Warwick Etingof - Kazhdan quantization of Lie bialgebras II	Room 1
16:00 to 17:30	John Jones University of Warwick Deformation theory: exercise session	Room 1

Wednesday 20th February 2013
10:30 to 12:00	Pierre Lochak Institut de Mathématiques de Jussieu Moduli spaces of curves, curve complexes	Room 1
14:00 to 15:30	Pierre Lochak Institut de Mathématiques de Jussieu The Teichmueller lego	Room 1
16:00 to 17:30	Pierre Lochak Institut de Mathématiques de Jussieu Special Topic: Origamis	Room 1

Thursday 21st February 2013
14:00 to 16:00	Damien Calaque ETH Zürich Factorization algebras and formality theorems I	Room 1
16:00 to 17:00	Damien Calaque ETH Zürich Factorization algebras and formality theorems II	Room 1

Tuesday 26th February 2013
10:30 to 12:00	Damien Calaque ETH Zürich From associators to the Kashiwara-Vergne conjecture I (after Alekseev-Torossian)	Room 1
14:00 to 15:30	Damien Calaque ETH Zürich From associators to the Kashiwara-Vergne conjecture II (after Alekseev-Enriquez-Torossian)	Room 1
16:00 to 17:30	Damien Calaque ETH Zürich Deformation theory: exercise session	Room 1

Wednesday 27th February 2013
10:30 to 12:00	Leila Schneps Institut de Mathématiques de Jussieu Lie algebras I	Room 1
14:00 to 15:30	Leila Schneps Institut de Mathématiques de Jussieu Lie algebras II	Room 1
16:00 to 17:30	Leila Schneps Institut de Mathématiques de Jussieu Special Topic	Room 1

Thursday 28th February 2013
10:30 to 12:00	John Jones University of Warwick Proof of the Deligne conjecture after McClure-Smith	Room 2
14:00 to 16:00	Cohomology of braid groups and mapping class groups I	Room 1
16:30 to 17:00	Cohomology of braid groups and mapping class groups II	Room 1

Tuesday 5th March 2013
14:00 to 15:15	Benoit Fresse Université Lille 1 Introduction to E_n-operads and little discs operads (mini-course)	Room 2
15:45 to 17:00	Benoit Fresse Université Lille 1 Homotopy automorphisms of operads in topological spaces (mini-course)	Room 2

Wednesday 6th March 2013
10:30 to 12:00	Francis Brown IHES Iterated integrals and de Rham fundamental group of P^1 minus 3 points	Room 1
14:00 to 15:30	Francis Brown IHES Malcev completion and Betti fundamental group of P^1 minus 3 points	Room 1
16:00 to 17:30	Francis Brown IHES Discussion Session	Room 1

Thursday 7th March 2013
14:00 to 16:00	Teimuraz Pirashvili University of Leicester Polynomial functors on free groups	Room 1

Tuesday 12th March 2013
14:00 to 15:15	Benoit Fresse Université Lille 1 The rational homotopy theory of spaces (mini-course)	Room 2
15:45 to 17:00	Benoit Fresse Université Lille 1 The rational homotopy theory of operads (mini-course)	Room 2

Wednesday 13th March 2013
10:30 to 12:00	Francis Brown IHES The Ihara action on the motivic fundamental group of P^1 minus 3 points	Room 1
14:00 to 15:30	Francis Brown IHES Motivic multiple zeta values and Galois coaction	Room 1
16:00 to 17:30	Francis Brown IHES Discussion Session	Room 1

Thursday 14th March 2013
10:30 to 12:00	Ralph Kaufmann Indiana University-Purdue University Indianapolis Arcs as an effective model	Room 2
14:00 to 15:00	Tomohide Terasoma University of Tokyo Brown-Zagier relation for associators: I	Room 1
15:00 to 16:00	Tomohide Terasoma University of Tokyo Brown-Zagier relation for associators: II	Room 1

Tuesday 19th March 2013
14:00 to 16:00	Markus Spitzweck Universität Osnabrück The abelian category of mixed Tate motives with integer coefficients	Room 2

Wednesday 20th March 2013
10:30 to 12:00	Herbert Gangl Durham University Relations among Multiple Zeta Values I	Room 2
14:00 to 15:30	Herbert Gangl Durham University Double Zeta Values and Modular Forms	Room 2
16:00 to 17:30	Herbert Gangl Durham University Multiple Zeta Values: discussion session	Room 2

Thursday 21st March 2013
14:00 to 16:00	Ralph Kaufmann Indiana University-Purdue University Indianapolis Feynman categories	Room 2

Friday 22nd March 2013
14:00 to 16:00	P Lochak's informal discussion	Discussion Room

Tuesday 26th March 2013
10:30 to 12:00	Kentaro Ihara Osaka University Derivations for multiple zeta values	Room 2

Wednesday 27th March 2013
10:30 to 12:00	Don Zagier Max-Planck-Institut für Mathematik, Bonn Relations among multiple zeta values II	Room 2

Thursday 28th March 2013
14:00 to 16:00	Kentaro Ihara Osaka University Multiple L-functions of modular forms	Room 2

Thursday 18th April 2013
14:00 to 16:00	Don Zagier Max-Planck-Institut für Mathematik, Bonn Finite multiple zeta values	Room 2
16:00 to 18:00	Benjamin Enriquez University of Strasbourg A lower bound of a sub-quotient of the Lie algebra associated to Grothendieck-Teichmüller group	Room 2

Grothendieck-Teichmüller groups, deformation and operads

Organisers

Herbert Gangl Durham University
John Jones University of Warwick
Pierre Lochak Institut de Mathématiques de Jussieu
Bruno Vallette Université de Nice Sophia Antipolis
Nicholas Woodhouse University of Oxford

Speakers

Dror Bar-Natan University of Toronto
Francis Brown IHES
Damien Calaque ETH Zürich
Pierre Cartier IHES
Benjamin Enriquez University of Strasbourg
Giovanni Felder ETH Zürich
Benoit Fresse Université Lille 1
Herbert Gangl Durham University
Kentaro Ihara Osaka University
John Jones University of Warwick
Ralph Kaufmann Indiana University-Purdue University Indianapolis
Pierre Lochak Institut de Mathématiques de Jussieu
Sergei Merkulov Stockholm University
Ieke Moerdijk Radboud Universiteit Nijmegen
Teimuraz Pirashvili University of Leicester
Leila Schneps Institut de Mathématiques de Jussieu
Markus Spitzweck Universität Osnabrück
Tomohide Terasoma University of Tokyo
Bruno Vallette Université de Nice Sophia Antipolis
Don Zagier Max-Planck-Institut für Mathematik, Bonn

Show All

Grothendieck-Teichmüller groups, deformation and operads

Programme theme

Preprints

The derived Maurer-Cartan locus

Geometric higher groupoids and categories

An A$_\infty$ operad in spineless cacti

Untwisting a twisted Calabi-Yau algebra

Givental action is homotopy gauge symmetry

Equations of tropical varieties

Modular invariant of quantum tori

A$_\infty$-actions and recognition of relative loop spaces

On the equivalence between Lurie's model and the dendroidal model for infinity-operads

Homology of depth-graded motivic Lie algebras and koszulity

Strong homology, and closed geodesics on manifolds which are elliptic spaces

Workshops

Overview days for non-specialists

Higher structure 2013: operads and deformation theory

Grothendieck-Teichmüller theory and multiple zeta values

Higher structures in topology and number theory

Seminars

Organisers

Speakers

Supported By

Grothendieck-Teichmüller groups, deformation and operads

Programme theme

Preprints

The derived Maurer-Cartan locus

Geometric higher groupoids and categories

An A$_\infty$ operad in spineless cacti

Untwisting a twisted Calabi-Yau algebra

Givental action is homotopy gauge symmetry

Equations of tropical varieties

Modular invariant of quantum tori

A$_\infty$-actions and recognition of relative loop spaces

On the equivalence between Lurie's model and the dendroidal model for infinity-operads

Homology of depth-graded motivic Lie algebras and koszulity

Strong homology, and closed geodesics on manifolds which are elliptic spaces

Workshops

Overview days for non-specialists

Higher structure 2013: operads and deformation theory

Grothendieck-Teichmüller theory and multiple zeta values

Higher structures in topology and number theory

Seminars

Organisers

Speakers

Supported By

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