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

23.08.2021 09:00 - 17.09.2021 16:00

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.



Xavier Bekaert (U Tours)

Andreas Cap (U Vienna)

Stefan Fredenhagen (U Vienna)

Maxim Grigoriev (Lebedev Inst. & Lomonosov Moscow SU)

Alexei Kotov (U Hradec Králové)

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


ESI, Boltzmann Lecture Hall, Boltzmanngasse 9/2,1090 Wien