Nearly Parallel G2-Structures on 7-Manifolds - Associative 3-Folds in Aloff-Wallach Spaces

Explore the intricacies of nearly parallel G2-manifolds in this 56-minute lecture by Alexei Kovalev from the University of Cambridge. Delve into the mathematical definition of nearly parallel G2-structures on 7-manifolds, focusing on their representation through 3-forms and associated differential equations. Examine specific applications of these structures to Aloff-Wallach spaces and regular Sasaki-Einstein 7-manifolds. Discover a novel construction method and concrete examples of associative 3-folds, a unique class of minimal submanifolds, within these spaces. This collaborative research presentation, conducted with M. Fernández, A. Fino, and V. Muñoz, offers advanced insights into differential geometry and manifold theory for mathematics enthusiasts and researchers.