Explore a 56-minute lecture on vertex algebras derived from the Hull Strominger system, delivered by Mario Garcia Fernandez from UAM. Delve into the intricate world of manifolds with special geometric structures, examining their connections to Lie group actions from Berger's list. Investigate the intersections of differential geometry with complex and algebraic geometry, global analysis, theoretical physics, and symplectic geometry. Discover topics such as Monge-Ampère equations, special holonomy, quaternionic geometry, twistor theory, non-Kähler complex manifolds, harmonic maps, Einstein and soliton metrics, homogeneous spaces, integrable systems, gauge theory, geometric flows, and mathematical string- and M-theory. Gain insights from this talk, part of a broader conference organized by esteemed mathematicians at the Instituto de Matemática Pura e Aplicada in Rio de Janeiro.