Coassociative Fibrations in G2 Geometry

Explore the fascinating world of G2 geometry in this 58-minute lecture by Alexei Kovalev from the University of Cambridge. Delve into the unique properties of the Euclidean space R7 and its G2 structure, which allows for the definition of intriguing submanifolds. Focus on coassociative 4-folds, a class of submanifolds that are volume-minimizing when the G2 structure is torsion-free. Discover the parallels between coassociative submanifolds and special Lagrangian submanifolds of Calabi-Yau manifolds. Learn about the role of differential forms in establishing G2 geometry in 7 dimensions and explore the deformation theory of coassociative submanifolds. Gain insights into various constructions where deformation families "fill" the ambient 7-manifold M, creating fibrations of M by coassociative submanifolds with some singular fibers. This lecture, part of the IMSAC Consortium, offers a deep dive into advanced mathematical concepts at the intersection of geometry and topology.