Geometry for Higher Spin Gravity: Conformal Structures, PDEs, and Q-manifolds

The idea is to bring together people studying mathematical aspects of higher- spin gravity, and experts on the several geometries which appeared in this construction, in particular conformal geometry, the geometry of partial differential equations, as well as differential graded geometry.

The construction of consistent interactions among gauge fields of spin higher than two is a notoriously difficult challenge. Each time some of the obstacles were overcome, various modern mathematical notions played a crucial role in the construction. Although higher-spin geometry in itself might presently remain somewhat elusive, various fundamental mathematical objects have already appeared in higher-spin gravity, originating from conformal geometry (Cartan connections, tractor bundles, Fefferman-Graham ambient metric, etc), the geometry of Partial Differential Equations (e.g. infinite jet bundles and their Cartan distributions), differential graded geometry (such as Q-manifolds, Batalin-Vilkovisky and Becchi-Rouet-Stora-Tyutin formalisms, Alexandrov-Kontsevich-Schwarz-Zaboronsky sigma models) and deformation quantization (for instance Fedosov-like connection, formality theorems, deformation theory, etc). The deep relation between higher-spin gravity and important topics of contemporary mathematics might keep some surprises in store and shed new light on each other. This promises fruitful exchanges from which both communities will benefit.

In addition to research talks by participants it is planned to have several introductory minicourses, including:

 

1st week (23/08-27/08):

I. Anderson, Introduction to the variational bicomplex
A. Cap, Cartan geometry 
A. Cattaneo, An introduction to the BV-BFV formalism
E. Skvortsov, Conformal higher spin gravities and holography

2nd week (30/08-03/09):

M. Eastwood, Conformal differential geometry - the ambient metric and tractor connection
M. Henneaux,   Introduction to asymptotic symmetries 
A. Mikhailov, Q-manifolds and pure spinors
M. A. Vasiliev, Introduction to HS fields and interactions in AdS

3rd week (06/09-10/09):

T. Adamo, Twistors, ambitwistors and amplitudes
M. Eastwood, Conformal differential geometry - the ambient metric and tractor connection
J. Krasil'shchik, A. Verbovetsky, Geometry of PDEs: an overview 

4th week (13/09-17/09):

G. Barnich, Photons and gravitons in a Casimir box
R. Gover, Boundary calculus
B. Kruglikov, Lie equations, Cartan bundles, Tanaka theory and differential invariants

Aug. 23, 2021
09:30 — 10:30
Registration
10:30 — 11:00
Coffee Break
11:00 — 12:00
Lecture by Andreas Cap (U Vienna)
Cartan Geometries 1
12:00 — 14:00
Lunch
14:00 — 15:00
Lecture by Eugene Skvortsov (U Mons)
Conformal higher spin gravities and holography, 1
15:00 — 15:30
Coffee break
15:30 — 16:30
Kirill Krasnov (U of Nottingham)
Self-dual Yang-Mills and self-dual gravity
Aug. 24, 2021
09:30 — 10:30
Lecture by Andreas Cap (U Vienna)
Cartan geometries 2
10:30 — 11:00
Coffee break
11:00 — 12:00
12:00 — 14:00
Lunch
15:00 — 15:30
Coffee break
Aug. 25, 2021
09:30 — 10:30
10:30 — 11:00
Coffee break
12:00 — 14:00
Lunch
14:00 — 15:00
15:00 — 15:30
Coffee break
15:30 — 16:30
Aug. 26, 2021
10:30 — 11:00
Coffee break
11:00 — 12:00
12:00 — 14:00
Lunch
14:00 — 15:00
Lecture

Alberto Cattaneo (University of Zurich) An introduction to the BV-BFV formalism, 1

15:00 — 15:30
Coffee break
15:30 — 16:30
Lecture by Ian Anderson (Utah State U.)
Lecture 2: Variational Bicomplexes: Diverse Applications
Aug. 27, 2021
09:30 — 10:30
Lecture

Alberto Cattaneo (University of Zurich) An introduction to the BV-BFV formalism, 2

10:30 — 11:00
Coffee break
11:00 — 12:00
12:00 — 14:00
Lunch
14:00 — 15:00
Vladimir Salnikov (CNRS / U La Rochelle)
Some constructions from graded geometry
15:00 — 15:30
Coffee break
15:30 — 16:30
Alexander Voronov (U of Minnesota)
NQ-manifolds and homotopy Lie bialgebroids
Aug. 30, 2021
09:00 — 09:30
Registration
09:30 — 10:30
Lecture by Mikhail Vasiliev (Lebedev Physical Institute, Moscow)
Introduction to HS fields and interactions in AdS I
Recording

(online)

10:30 — 11:00
Coffee break
11:00 — 12:00
12:00 — 14:00
Lunch
14:00 — 15:00
Lecture

A. Cattaneo (University of Zurich) An introduction to the BV-BFV formalism 3

15:00 — 15:30
Coffee break
Aug. 31, 2021
09:30 — 10:30
Lecture by Mikhail Vasiliev (Lebedev Physical Institute, Moscow)
Introduction to HS fields and interactions in AdS II
Recording

(online)

10:30 — 11:00
Coffee break
11:00 — 12:00
Lecture by Marc Henneaux (ULB, Brussels)
Introduction to asymptotic symmetries - Examples
12:00 — 14:00
Lunch
14:15 — 15:15
Michele Schiavina (ETH Zürich)
BV-BFV Approach to General Relativity
15:15 — 15:45
Coffee break
Sept. 1, 2021
09:30 — 10:30
10:30 — 11:00
Coffee break
11:00 — 12:00
12:00 — 14:00
Lunch
14:00 — 15:00
Lecture by Andrei Mikhailov (IFT UNESP, Sao Paolo)
Lecture 1 : Classical phase space of bosonic string is a Q-manifold
Slides

(online)

15:00 — 15:30
Coffee break
18:30
Conference dinner
Sept. 2, 2021
09:30 — 10:30
Mikhail Vasiliev (Lebedev Physical Institute, Moscow)
Recent results in higher-spin gauge theory
Recording

(online)

10:30 — 11:00
Coffee break
11:00 — 12:00
12:00 — 14:00
Lunch
14:00 — 15:00
Lecture by Andrei Mikhailov (IFT UNESP, Sao Paolo)
Lecture 2: Target space of pure spinor superstring is a Q-manifold
Slides

(online)

15:00 — 15:30
Coffee break
15:30 — 16:30
Poster session
Sept. 3, 2021
09:30 — 10:30
10:30 — 11:00
Coffee break
11:00 — 12:00
12:00 — 14:00
Lunch
14:00 — 15:00

(online)

15:00 — 15:30
Coffee break
15:30 — 16:30
Sept. 6, 2021
09:00 — 09:30
Registration
09:30 — 10:30
10:30 — 11:00
Coffee break
11:00 — 12:00
Lecture by Tim Adamo (U Edinburgh)
Lecture 1: Twistors and amplitudes
Recording

(online)

12:00 — 14:00
Lunch
14:00 — 15:00
Karapet Mkrtchyan (Imperial College, London)
Democratic (N)ED
15:00 — 15:30
Coffee break
Sept. 7, 2021
09:30 — 10:30
Jan Slovak (Masaryk U, Brno)
Calculus on Symplectic Manifolds
10:30 — 11:00
Coffee break
11:00 — 12:00
Lecture by Tim Adamo (U Edinburgh)
Lecture 2: Ambitwistors and amplitudes
Recording

(online)

12:00 — 14:00
Lunch
15:00 — 15:30
Coffee break
Sept. 8, 2021
10:30 — 11:00
Coffee break
11:00 — 12:00
12:00 — 14:00
Lunch
14:00 — 15:00
Lecture by Joseph Krasil’shchik (IUM)
Geometry of PDEs: an overview

(online)

15:00 — 15:30
Coffee break
15:30 — 16:30
Andrew Waldron (UC Davis)
Quantization of Contact Structures
Recording

(online)

Sept. 9, 2021
10:30 — 11:00
Coffee break
11:00 — 12:00
Branislav Jurco (Charles U, Prague)
TBA
12:00 — 14:00
Lunch
14:00 — 15:00
Lecture by Joseph Krasil’shchik (IUM)
Geometry of PDEs: an overview

(online)

15:00 — 15:30
Coffee break
15:30 — 16:30
Sept. 10, 2021
10:30 — 11:00
Coffee break
12:00 — 14:00
Lunch
14:00 — 15:00
Lecture by Alexander Verbovetsky (IUM)
Geometry of PDEs: an overview
Recording

(online)

15:00 — 15:30
Coffee break
15:30 — 16:00
Dr. Tim Adamo (U Edinburgh)

Informal extra lecture:  Ambitwistors 
(online)

Sept. 13, 2021
09:00 — 09:30
Registration
09:30 — 10:30
Lecture by Rod Gover (University of Auckland)
Boundary calculus in conformal geometry. Lecture 1
10:30 — 11:00
Coffee break
12:00 — 14:00
Lunch
14:00 — 15:00
15:00 — 15:30
Coffee break
Sept. 14, 2021
09:30 — 10:30
Lecture by Rod Gover (University of Auckland)
Boundary calculus in conformal geometry. Lecture 2
Recording

(online)

10:30 — 11:00
Coffee break
12:00 — 14:00
Lunch
14:00 — 15:00
Euihun Joung (Kyung Hee U, Seoul)
Unfolding Conformal Geometry
Recording

(online)

15:30 — 16:30
Sept. 15, 2021
10:30 — 11:00
Coffee break
12:00 — 14:00
Lunch
15:00 — 15:30
Coffee break
15:30 — 16:30
Jan Vysoky (CTU Prague)
Graded Courant Algebroids
Sept. 16, 2021
10:30 — 11:00
Coffee break
11:00 — 12:00
Lecture by Glenn Barnich (ULB, Brussels)
Lecture 3: Gravitons in a Casimir box
12:00 — 14:00
Lunch
14:00 — 15:00
15:00 — 15:30
Coffee break
Sept. 17, 2021
09:30 — 10:30
10:30 — 11:00
Coffee break
11:00 — 12:00
12:00 — 14:00
Lunch
15:00 — 15:30
Coffee break
This event has no subevents associated to it.

Organizers

Name Affiliation
Xavier Bekaert University of Tours
Andreas Cap University of Vienna
Stefan Fredenhagen University of Vienna
Maxim Grigoriev Lebedev Physical Institute & Lomonosov Moscow State University
Alexei Kotov University of Hradec Králové

Attendees

Name Affiliation
Tim Adamo University of Edinburgh
Konstantin Alkalaev Lebedev Physical Institute & Lomonosov Moscow State University
Ian Anderson Utah State University
Glenn Barnich Free University of Brussels
Thomas Basile University of Mons
Klaus Bering Masaryk University
Nicolas Boulanger University of Mons
Andrea Campoleoni University of Mons
Alberto Cattaneo University of Zürich
Luca Ciambelli Free University of Brussels
Oscar Cosserat University of La Rochelle
David De Filippi University of Mons
Arnaud Delfante University of Mons
Ivan Dneprov Lomonosov Moscow State University
Laura Donnay Technical University of Vienna
Boris Doubrov Belarusian State University
Cristina Draper Fontanals Universidad de Malaga
Michael Eastwood University of Adelaide
Dario Francia Università Roma Tre
Jordan Francois University of Mons
Jordi Frias Lomonosov Moscow State University
Oscar Fuentealba Free University of Brussels
Olga Gelfond Lebedev Physical Institute
Rod Gover University of Auckland
Vyacheslav Gritsaenko Moscow Institute of Physics and Technology
Daniel Grumiller Technical University of Vienna
Aliaksandr Hancharuk University of Lyon
Christoph Harrach University of Vienna
Marc Henneaux Free University of Brussels
Yannick Herfray Free University of Brussels
Daniel Hutchings University of Western Australia
Carlo Iazeolla Guglielmo Marconi University
Noriaki Ikeda Ritsumeikan University
Euihun Joung Kyung Hee University
Branislav Jurco Charles University Prague
Igor Khavkine Institute of Mathematics of the Czech Academy of Sciences
Yvette Kosmann-Schwarzbach retired from Ecole polytechnique
Niels Kowalzig University Federico II of Napoli
Joseph Krasil’shchik Independent University of Moscow
Kirill Krasnov University of Nottingham
Olaf Krüger University of Vienna
Boris Kruglikov University of Tromsø
Svatopluk Krysl Charles University Prague
Sergei Kuzenko University of Western Australia
Kristiansen Lara Universidad de Chile
Camille Laurent-Gengoux University of Lorraine
Rob Leigh University of Illinois at Urbana-Champaign
Thomas Leistner University of Adelaide
Iva Lovrekovic Technical University of Vienna
Sucheta Majumdar Free University of Brussels
Omid Makhmali Polish Academy of Sciences
Chrysoula Markou Max Planck Institute for Physics
Mikhail Markov Lomonosov Moscow State University
Javier Matulich Fabres Free University of Brussels
Ruslan Metsaev Lebedev Physical Institute
Andrei Mikhailov IFT UNESP
Nikita Misuna Albert Einstein Institut
Karapet Mkrtchyan Imperial College London
Pavel Mnev University of Notre Dame du Lac
Kevin Morand Sogang University
Timothy Moy University of Adelaide
Turmoli Neogi Free University of Brussels
Katharina Neusser Masaryk University
Francisco José Palomo Universidad de Malaga
Enrico Parisini University of Southampton
Noémie Parrini University of Mons
Mateo Paulišić University of Rijeka
Simon Pekar University of Mons
Alfredo Perez Centro de Estudios Cientificos
Michael Ponds University of Western Australia
Dmitry Ponomarev Lomonosov Moscow State University
Stefan Prohazka University of Edinburgh
Nicolai Reshetikhin University of California, Berkeley
Jan Rosseel Ruđer Bošković Institute
Dmitrii Rudinskii Lomonosov Moscow State University
Romain Ruzziconi Technical University of Vienna
Leonid Ryvkin University of Göttingen
Ivo Sachs Ludwig-Maximilians-University Munich
Katja Sagerschnig Polish Academy of Sciences
Vladimir Salnikov CNRS / U La Rochelle
Jakob Salzer Harvard University
Henning Samtleben Ecole Normale Superieure de Lyon
Andrea Santi The Arctic University of Norway
Paolo Saracco Free University of Brussels
Michele Schiavina ETH Zürich
Pavel Sereda Lomonosov Moscow State University
Alexey Sharapov National Research Tomsk State University
Georgy Sharygin Lomonosov Moscow State University
Ekaterina Shemyakova University of Toledo
Eugene Skvortsov University of Mons
Jan Slovak Masaryk University
Harold Steinacker University of Vienna
Thomas Strobl University of Lyon
Per Sundell Universidad Andrés Bello
Tom Sutherland University of Vienna
Arman Taghavi-Chabert University of Warsaw
Dennis The University of Tromsø
Ricardo Troncoso Centro de Estudios Cientificos
Arkady Tseytlin Imperial College London
Mirian Tsulaia Okinawa Institute of Science and Technology
Mikhail Vasiliev Lebedev Physical Institute
Alexander Verbovetsky Independent University of Moscow
Luca Vitagliano University of Salerno
Alexander Voronov University of Minnesota
Theodore Voronov University of Manchester
Ivan Vuković University of Rijeka
Jan Vysoky Czech Technical University Prague
Andrew Waldron University of California, Davis
Raphaela Wutte Technical University of Vienna
Alexander Yan Lomonosov Moscow State University
Yihao Yin Nanjing University of Aeronautics and Astronautics
Lenka Zalabová University of South Bohemia
Preview of Andreas Cap - Cartan Geometries 1
Andreas Cap (U Vienna): Cartan Geometries 1
Aug. 23, 2021 11:00 — 12:00
Preview of Andreas Cap - Cartan geometries 2
Andreas Cap (U Vienna): Cartan geometries 2
Aug. 24, 2021 09:30 — 10:30
Preview of Eugene Skvortsov - Conformal higher spin gravities and holography, 2
Eugene Skvortsov (U Mons): Conformal higher spin gravities and holography, 2
Aug. 24, 2021 11:00 — 12:00
Preview of Henning Samtleben - Introduction to exceptional field theory
Henning Samtleben (ENS Lyon): Introduction to exceptional field theory
Aug. 25, 2021 09:30 — 10:30
Preview of Chrysoula Markou - Extracting Bigravity from String Amplitudes
Chrysoula Markou (MPP, Munich): Extracting Bigravity from String Amplitudes
Aug. 25, 2021 14:00 — 15:00
Preview of Daniel Grumiller - Higher spins and non-AdS holography in lower dimensions
Daniel Grumiller (TU Vienna): Higher spins and non-AdS holography in lower dimensions
Aug. 26, 2021 11:00 — 12:00
Preview of Ian Anderson - Lecture 2: Variational Bicomplexes: Diverse Applications
Ian Anderson (Utah State U.): Lecture 2: Variational Bicomplexes: Diverse Applications
Aug. 26, 2021 15:30 — 16:30
Preview of Eugene Skvortsov - Higher spin gravities and holography
Eugene Skvortsov (U Mons): Higher spin gravities and holography
Aug. 27, 2021 11:00 — 12:00
Preview of Vladimir Salnikov - Some constructions from graded geometry
Vladimir Salnikov (CNRS / U La Rochelle): Some constructions from graded geometry
Aug. 27, 2021 14:00 — 15:00
Preview of Alexander Voronov - NQ-manifolds and homotopy Lie bialgebroids
Alexander Voronov (U of Minnesota): NQ-manifolds and homotopy Lie bialgebroids
Aug. 27, 2021 15:30 — 16:30
Preview of Mikhail Vasiliev - Introduction to HS fields and interactions in AdS I
Mikhail Vasiliev (Lebedev Physical Institute, Moscow): Introduction to HS fields and interactions in AdS I
Aug. 30, 2021 09:30 — 10:30
Preview of Marc Henneaux - Introduction to asymptotic symmetries - General formalism
Marc Henneaux (ULB, Brussels): Introduction to asymptotic symmetries - General formalism
Aug. 30, 2021 11:00 — 12:00
Preview of Mikhail Vasiliev - Introduction to HS fields and interactions in AdS II
Mikhail Vasiliev (Lebedev Physical Institute, Moscow): Introduction to HS fields and interactions in AdS II
Aug. 31, 2021 09:30 — 10:30
Preview of Marc Henneaux -  Introduction to asymptotic symmetries - Examples
Marc Henneaux (ULB, Brussels): Introduction to asymptotic symmetries - Examples
Aug. 31, 2021 11:00 — 12:00
Preview of Michele Schiavina - BV-BFV Approach to General Relativity
Michele Schiavina (ETH Zürich): BV-BFV Approach to General Relativity
Aug. 31, 2021 14:15 — 15:15
Preview of Sergei Kuzenko - Duality-invariant conformal higher-spin models
Sergei Kuzenko (UWA, Perth): Duality-invariant conformal higher-spin models
Sept. 1, 2021 09:30 — 10:30
Preview of Marc Henneaux - The BMS (super)algebra at spatial infinity
Marc Henneaux (ULB, Brussels): The BMS (super)algebra at spatial infinity
Sept. 1, 2021 11:00 — 12:00
Preview of Mikhail Vasiliev - Recent results in higher-spin gauge theory
Mikhail Vasiliev (Lebedev Physical Institute, Moscow): Recent results in higher-spin gauge theory
Sept. 2, 2021 09:30 — 10:30
Preview of Andrea Campoleoni - On Carrollian and Galilean higher-spin algebras
Andrea Campoleoni (U Mons): On Carrollian and Galilean higher-spin algebras
Sept. 2, 2021 11:00 — 12:00
Preview of Dmitry Ponomarev - Spinor-helicity formalism for higher-spin holography
Dmitry Ponomarev (Lomonosov Moscow SU): Spinor-helicity formalism for higher-spin holography
Sept. 3, 2021 11:00 — 12:00
Preview of Tim Adamo - Lecture 1: Twistors and amplitudes
Tim Adamo (U Edinburgh): Lecture 1: Twistors and amplitudes
Sept. 6, 2021 11:00 — 12:00
Preview of Karapet Mkrtchyan - Democratic (N)ED
Karapet Mkrtchyan (Imperial College, London): Democratic (N)ED
Sept. 6, 2021 14:00 — 15:00
Preview of Jan Slovak - Calculus on Symplectic Manifolds
Jan Slovak (Masaryk U, Brno): Calculus on Symplectic Manifolds
Sept. 7, 2021 09:30 — 10:30
Preview of Tim Adamo - Lecture 2: Ambitwistors and amplitudes
Tim Adamo (U Edinburgh): Lecture 2: Ambitwistors and amplitudes
Sept. 7, 2021 11:00 — 12:00
Preview of Dario Francia - Lagrangian double copy to cubic order
Dario Francia (U Roma III): Lagrangian double copy to cubic order
Sept. 8, 2021 11:00 — 12:00
Preview of Andrew Waldron - Quantization of Contact Structures
Andrew Waldron (UC Davis): Quantization of Contact Structures
Sept. 8, 2021 15:30 — 16:30
Preview of Per Sundell - Quantum field theory as a topological sigma.model
Per Sundell (UNAB, Santiago): Quantum field theory as a topological sigma.model
Sept. 9, 2021 15:30 — 16:30
Preview of Alexander Verbovetsky - Geometry of PDEs: an overview
Alexander Verbovetsky (IUM): Geometry of PDEs: an overview
Sept. 10, 2021 14:00 — 15:00
Preview of Rod Gover - Boundary calculus in conformal geometry. Lecture 1
Rod Gover (University of Auckland): Boundary calculus in conformal geometry. Lecture 1
Sept. 13, 2021 09:30 — 10:30
Preview of Rod Gover - Higher conformal fundamental forms and the asymptotically Poincare-Einstein Condition
Rod Gover (University of Auckland): Boundary calculus in conformal geometry. Lecture 2
Sept. 14, 2021 09:30 — 10:30
Preview of Euihun Joung - Unfolding Conformal Geometry
Euihun Joung (Kyung Hee U, Seoul): Unfolding Conformal Geometry
Sept. 14, 2021 14:00 — 15:00
Preview of Omid Makhmali - Einstein-Weyl-like conditions and causal structures in dimension three
Omid Makhmali (Polish Academy of Science, Warsaw): Einstein-Weyl-like conditions and causal structures in dimension three
Sept. 14, 2021 15:30 — 16:30
Preview of Jan Vysoky - Graded Courant Algebroids
Jan Vysoky (CTU Prague): Graded Courant Algebroids
Sept. 15, 2021 15:30 — 16:30
Preview of Glenn Barnich - Lecture 3: Gravitons in a Casimir box
Glenn Barnich (ULB, Brussels): Lecture 3: Gravitons in a Casimir box
Sept. 16, 2021 11:00 — 12:00
Preview of Yannick Herfray - Tractor geometry of null-Infinity and gravitational radiations
Yannick Herfray (ULB, Brussels): Tractor geometry of null-Infinity and gravitational radiations
Sept. 16, 2021 14:00 — 15:00
Preview of Boris Kruglikov - Super-symmetry of geometric structures
Boris Kruglikov (UiT): Super-symmetry of geometric structures
Sept. 17, 2021 09:30 — 10:30
Preview of Luca Vitagliano - Multiplicative Connections on Lie Groupoids
Luca Vitagliano (UNISA): Multiplicative Connections on Lie Groupoids
Sept. 17, 2021 11:00 — 12:00
At a glance
Type:
Thematic Programme
When:
Aug. 23, 2021 — Sept. 17, 2021
Where:
ESI Boltzmann Lecture Hall
Organizer(s):
Xavier Bekaert (U Tours)
Andreas Cap (U Vienna)
Stefan Fredenhagen (U Vienna)
Maxim Grigoriev (Lebedev Inst. & Lomonosov Moscow SU)
Alexei Kotov (U Hradec Králové)