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):

T. Adamo, Twistors, ambitwistors and amplitudes
I. Anderson, Introduction to the variational bicomplex
A. Cattaneo, An introduction to the BV-BFV formalism
M. Vasiliev, Introduction to HS fields and interactions in AdS

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
E. Skvortsov, HS holography and conformal HS

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

A. Cap, Cartan geometry 
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, Casimir effect and modular invariance for gravity and higher spin fields
R. Gover, Boundary calculus
B. Kruglikov, Lie equations, Cartan bundles, Tanaka theory and differential invariants


Coming soon.

This event has no subevents associated to it.
  • Tim Adamo (U Edinburgh)
  • Ian Anderson (Utah State U.)
  • Glenn Barnich (ULB, Brussels)
  • Xavier Bekaert (U Tours) — Organizer
  • Nicolas Boulanger (U Mons)
  • Andrea Campoleoni (U Mons)
  • Andreas Cap (U Vienna) — Organizer
  • Alberto Cattaneo (U Zürich)
  • David De Filippi (U Mons)
  • Arnaud Delfante (U Mons)
  • Ivan Dneprov (Lomonosov Moscow SU)
  • Boris Doubrov (BSU)
  • Dario Francia (U Roma III)
  • Jordan Francois (U Mons)
  • Stefan Fredenhagen (U Vienna) — Organizer
  • Jordi Frias (Lomonosov Moscow SU)
  • Olga Gelfond (Lebedev Physical Institute, Moscow)
  • Rod Gover (University of Auckland)
  • Maxim Grigoriev (Lebedev Inst. & Lomonosov Moscow SU) — Organizer
  • Aliaksandr Hancharuk (U Lyon)
  • Marc Henneaux (ULB, Brussels)
  • Yannick Herfray (ULB, Brussels)
  • 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)
  • Kirill Krasnov (U of Nottingham)
  • Boris Kruglikov (UiT)
  • Svatopluk Krysl (Charles U, Prague)
  • Sergei Kuzenko (UWA, Perth)
  • Iva Lovrekovic (TU Vienna)
  • Omid Makhmali (Polish Academy of Science, Warsaw)
  • Nikita Misuna (AEI Golm)
  • Noémie Parrini (U Mons)
  • Simon Pekar (U Mons)
  • Michael Ponds (UWA, Perth)
  • Dmitry Ponomarev (Lomonosov Moscow SU)
  • Nicolai Reshetikhin (UC, Berkeley)
  • Dmitrii Rudinskii (Lomonosov Moscow SU)
  • Leonid Ryvkin (U Göttingen)
  • Katja Sagerschnig (Polish Academy of Science, Warsaw)
  • Vladimir Salnikov (CNRS, Paris)
  • 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)
  • Eugene Skvortsov (U Mons)
  • Jan Slovak (Masaryk U, Brno)
  • Harold Steinacker (U Vienna)
  • Dennis The (UiT)
  • Arkady Tseytlin (Imperial College, London)
  • Mikhail Vasiliev (Lebedev Physical Institute, Moscow)
  • Alexander Verbovetsky (IUM)
  • Luca Vitagliano (UNISA)
  • Alexander Voronov (U of Minnesota)
  • Theodore Voronov (U Manchester)
  • Jan Vysoky (CTU Prague)
  • Andrew Waldron (UC Davis)
  • Alexander Yan (Lomonosov Moscow SU)
At a glance
Thematic Programme
Aug. 23, 2021 — Sept. 17, 2021
ESI Boltzmann Lecture Hall
Xavier Bekaert (U Tours)
Andreas Cap (U Vienna)
Stefan Fredenhagen (U Vienna)
Maxim Grigoriev (Lebedev Inst. & Lomonosov Moscow SU)
Alexei Kotov (U Hradec Králové)