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
Slides

(online)

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
Slides

(online)

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
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

(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

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

(online)

15:30 — 16:30
Omid Makhmali (Polish Academy of Science, Warsaw)
Einstein-Weyl-like conditions and causal structures in dimension three
Sept. 15, 2021
09:30 — 10:30
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.
  • Tim Adamo (U Edinburgh)
  • Konstantin Alkalaev (Lebedev Inst. & Lomonosov Moscow SU)
  • Ian Anderson (Utah State U.)
  • Glenn Barnich (ULB, Brussels)
  • Thomas Basile (Kyung Hee U, Seoul)
  • Xavier Bekaert (U Tours) — Organizer
  • Klaus Bering (Masaryk U, Brno)
  • Nicolas Boulanger (U Mons)
  • Andrea Campoleoni (U Mons)
  • Andreas Cap (U Vienna) — Organizer
  • Alberto Cattaneo (U Zürich)
  • Luca Ciambelli (ULB, Brussels)
  • Oscar Cosserat (U of La Rochelle)
  • David De Filippi (U Mons)
  • Arnaud Delfante (U Mons)
  • Ivan Dneprov (Lomonosov Moscow SU)
  • Laura Donnay (TU Vienna)
  • Boris Doubrov (BSU)
  • Cristina Draper Fontanals (Malaga U)
  • Michael Eastwood (Adelaide U.)
  • Dario Francia (U Roma III)
  • Jordan Francois (U Mons)
  • Stefan Fredenhagen (U Vienna) — Organizer
  • Jordi Frias (Lomonosov Moscow SU)
  • Oscar Fuentealba (ULB, Brussels)
  • Olga Gelfond (Lebedev Physical Institute, Moscow)
  • Rod Gover (University of Auckland)
  • Maxim Grigoriev (Lebedev Inst. & Lomonosov Moscow SU) — Organizer
  • Vyacheslav Gritsaenko (MIPT)
  • Daniel Grumiller (TU Vienna)
  • Aliaksandr Hancharuk (U Lyon)
  • Christoph Harrach (U Vienna)
  • Marc Henneaux (ULB, Brussels)
  • Yannick Herfray (ULB, Brussels)
  • Daniel Hutchings (UWA, Perth)
  • Carlo Iazeolla (G. Marconi University)
  • Noriaki Ikeda (Ritsumeikan U, Kusatsu)
  • Euihun Joung (Kyung Hee U, Seoul)
  • Branislav Jurco (Charles U, Prague)
  • Igor Khavkine (IM CAS)
  • Yvette Kosmann-Schwarzbach (retired)
  • Alexei Kotov (U Hradec Králové) — Organizer
  • Niels Kowalzig (U Napoli)
  • Joseph Krasil’shchik (IUM)
  • Kirill Krasnov (U of Nottingham)
  • Olaf Krüger (U Vienna)
  • Boris Kruglikov (UiT)
  • Svatopluk Krysl (Charles U, Prague)
  • Sergei Kuzenko (UWA, Perth)
  • Kristiansen Lara (U de Chile, Santiago)
  • Camille Laurent-Gengoux (U Lorraine)
  • Rob Leigh (U Illinois)
  • Thomas Leistner (Adelaide U.)
  • Iva Lovrekovic (TU Vienna)
  • Sucheta Majumdar (ULB, Brussels)
  • Omid Makhmali (Polish Academy of Science, Warsaw)
  • Chrysoula Markou (MPP, Munich)
  • Mikhail Markov (Lomonosov Moscow SU)
  • Javier Matulich Fabres (ULB, Brussels)
  • Ruslan Metsaev (Lebedev Physical Institute, Moscow)
  • Andrei Mikhailov (IFT UNESP, Sao Paolo)
  • Nikita Misuna (AEI Golm)
  • Karapet Mkrtchyan (Imperial College, London)
  • Pavel Mnev (Notre Dame)
  • Kevin Morand (Sogang U)
  • Timothy Moy (Adelaide U.)
  • Turmoli Neogi (ULB, Brussels)
  • Katharina Neusser (Masaryk U, Brno)
  • Francisco José Palomo (Malaga U)
  • Enrico Parisini (U Southampton)
  • Noémie Parrini (U Mons)
  • Mateo Paulišić (U Rijeka)
  • Simon Pekar (U Mons)
  • Alfredo Perez (CECS, Valdivia)
  • Michael Ponds (UWA, Perth)
  • Dmitry Ponomarev (Lomonosov Moscow SU)
  • Stefan Prohazka (U Edinburgh)
  • Nicolai Reshetikhin (UC, Berkeley)
  • Jan Rosseel (U Vienna)
  • Dmitrii Rudinskii (Lomonosov Moscow SU)
  • Romain Ruzziconi (TU Vienna)
  • Leonid Ryvkin (U Göttingen)
  • Ivo Sachs (LMU Munich)
  • Katja Sagerschnig (Polish Academy of Science, Warsaw)
  • Vladimir Salnikov (CNRS, Paris)
  • Jakob Salzer (Harvard U, Cambridge)
  • Henning Samtleben (ENS Lyon)
  • Andrea Santi (Arctic U)
  • Paolo Saracco (ULB, Brussels)
  • Michele Schiavina (ETH Zürich)
  • Pavel Sereda (Lomonosov Moscow SU)
  • Alexey Sharapov (Tomsk State University)
  • Georgy Sharygin (Lomonosov Moscow SU)
  • Ekaterina Shemyakova (UToledo)
  • Eugene Skvortsov (U Mons)
  • Jan Slovak (Masaryk U, Brno)
  • Harold Steinacker (U Vienna)
  • Thomas Strobl (U Lyon)
  • Per Sundell (UNAB, Santiago)
  • Tom Sutherland (U Vienna)
  • Arman Taghavi-Chabert (U Warsaw)
  • Dennis The (UiT)
  • Ricardo Troncoso (CECS, Valdivia)
  • Arkady Tseytlin (Imperial College, London)
  • Mirian Tsulaia (OIST)
  • Mikhail Vasiliev (Lebedev Physical Institute, Moscow)
  • Alexander Verbovetsky (IUM)
  • Luca Vitagliano (UNISA)
  • Alexander Voronov (U of Minnesota)
  • Theodore Voronov (U Manchester)
  • Ivan Vuković (U Rijeka)
  • Jan Vysoky (CTU Prague)
  • Andrew Waldron (UC Davis)
  • Raphaela Wutte (TU Vienna)
  • Alexander Yan (Lomonosov Moscow SU)
  • Yihao Yin (NUAA, Nanjing)
  • Lenka Zalabová (South Bohemia U)
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 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, Paris): 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 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 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 Jan Vysoky - Graded Courant Algebroids
Jan Vysoky (CTU Prague): Graded Courant Algebroids
Sept. 15, 2021 15:30 — 16:30
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)