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.

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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 (Lomonosov Moscow State U)
Alexei Kotov (U Hradec Králové)