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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI) via YouTube

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Explore advanced mathematical frameworks in this comprehensive workshop series covering the geometric foundations of higher spin gravity theories. Delve into Cartan geometries, conformal structures, and their applications to modern theoretical physics through expert lectures on variational bicomplexes, asymptotic symmetries, and holographic correspondences. Master the mathematical tools of Q-manifolds, BV-BFV formalism, and tractor calculus while examining their roles in higher-spin gauge theories and AdS/CFT holography. Investigate cutting-edge topics including twistor methods, spinor-helicity formalism, and the geometric aspects of gravitational radiation at null infinity. Learn about exceptional field theory, quantum spacetime effects, and the democratic formulation of supergravity theories through detailed presentations by leading researchers. Study the interplay between differential geometry and physics through discussions of Lie equations, Cartan bundles, multiplicative connections on Lie groupoids, and graded geometric structures. Examine practical applications ranging from Casimir effects and partition functions to the algebraic classification of conformal invariants and the geometric perspective on BMS symmetries.

Syllabus

Andreas Cap - Cartan Geometries 1
Andreas Cap - Cartan geometries 2
Eugene Skvortsov - Conformal higher spin gravities and holography, 2
Iva Lovrekovic - Holography of new conformal higher spin theories in three dimensions
Stefan Prohazka - Maximally symmetric spacetimes and their lower dimensional theories
Henning Samtleben - Introduction to exceptional field theory
Harold Steinacker - (Higher-spin) gravity as a quantum effect on quantum space-time
Chrysoula Markou - Extracting Bigravity from String Amplitudes
Ian Anderson - Lecture 1: Variational Bicomplexes: The First Variational Formula
Thomas Strobl - Gauge theories with and without group actions and equivalences between them
Daniel Grumiller - Higher spins and non-AdS holography in lower dimensions
Ian Anderson - Lecture 2: Variational Bicomplexes: Diverse Applications
Eugene Skvortsov - Higher spin gravities and holography
Vladimir Salnikov - Some constructions from graded geometry
Alexander Voronov - NQ-manifolds and homotopy Lie bialgebroids
Mikhail Vasiliev - Introduction to HS fields and interactions in AdS I
Marc Henneaux - Introduction to asymptotic symmetries - General formalism
Mikhail Vasiliev - Introduction to HS fields and interactions in AdS II
Marc Henneaux - Introduction to asymptotic symmetries - Examples
Michele Schiavina - BV-BFV Approach to General Relativity
Sergei Kuzenko - Duality-invariant conformal higher-spin models
Marc Henneaux - The BMS (super)algebra at spatial infinity
Svatopluk Krysl - Differential operators on bundles invariant with respect to compact operators
Mikhail Vasiliev - Recent results in higher-spin gauge theory
Andrea Campoleoni - On Carrollian and Galilean higher-spin algebras
Michael Eastwood - Conformal differential geometry - the ambient metric and tractor connection 1
Dmitry Ponomarev - Spinor-helicity formalism for higher-spin holography
Pavel Mnev - Effective BV action for Chern-Simons theory on cylinders
Michael Eastwood - Conformal differential geometry - the ambient metric and tractor connection 2
Tim Adamo - Lecture 1: Twistors and amplitudes
Karapet Mkrtchyan - Democratic (N)ED
Jan Slovak - Calculus on Symplectic Manifolds
Tim Adamo - Lecture 2: Ambitwistors and amplitudes
Igor Khavkine - Homotopy transfer for conserved currents and rigid symmetries in gauge theories
Dario Francia - Lagrangian double copy to cubic order
Andrew Waldron - Quantization of Contact Structures
Per Sundell - Quantum field theory as a topological sigma.model
Boris Doubrov - Non-regular parabolic geometries via the notion of bi-filtered manifolds
Yannick Herfray - BMS symmetries and "asymptotic gravity vacua" from a geometric perspective
Alexander Verbovetsky - Geometry of PDEs: an overview
Rod Gover - Boundary calculus in conformal geometry. Lecture 1
Glenn Barnich - From finite temperature Casimir effect to massless scalar field partition functions
Rod Gover - Higher conformal fundamental forms and the asymptotically Poincare-Einstein Condition
Glenn Barnich - Massless scalar field partition functions & real analytic Eisenstein series
Euihun Joung - Unfolding Conformal Geometry
Omid Makhmali - Einstein-Weyl-like conditions and causal structures in dimension three
Rod Gover - Higher conformal fundamental forms and the asymptotically Poincare-Einstein Condition
Boris Kruglikov - Lie equations, Cartan bundles, Tanaka theory and differential invariants 1
Nicolas Boulanger - Algebraic classification of conformal invariants
Jan Vysoky - Graded Courant Algebroids
Boris Kruglikov - Lie equations, Cartan bundles, Tanaka theory and differential invariants 2
Glenn Barnich - Lecture 3: Gravitons in a Casimir box
Yannick Herfray - Tractor geometry of null-Infinity and gravitational radiations
Boris Kruglikov - Super-symmetry of geometric structures
Luca Vitagliano - Multiplicative Connections on Lie Groupoids
Paolo Saracco - Mathematical overview of universal enveloping algebras