Special Holonomy and Geometric Structures on Complex Manifolds

Explore the intricate world of special holonomy and geometric structures on complex manifolds in this comprehensive lecture by Robert Bryant from Duke University. Delve into the century-long study of holonomy, examining how manifolds with special geometric structures are understood through actions of Lie groups from Berger's renowned list. Discover the deep connections between differential geometry and various fields including complex and algebraic geometry, global analysis, theoretical physics, and symplectic geometry. Investigate topics such as Monge-Ampère equations, quaternionic geometry, twistor theory, non-Kähler complex manifolds, harmonic maps, Einstein and soliton metrics, homogeneous spaces, integrable systems, gauge theory, geometric flows, and mathematical aspects of string- and M-theory. Gain insights from this presentation, part of a broader event organized by the Instituto de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro, featuring an esteemed organizing committee of international mathematicians.