Killing and Ricci-Hessian Equations in Pseudo-Kähler Geometry - Special Holonomy and Geometric Structures on Complex Manifolds

Explore a 58-minute lecture on Killing and Ricci-Hessian equations in (pseudo)Kähler geometry, delivered by Andrzej Derdzinski from Ohio State University. Delve into the world of manifolds with special geometric structures, examining their connections to Lie groups from Berger's list. Discover the intricate relationships between differential geometry and fields such as complex and algebraic geometry, global analysis, theoretical physics, and symplectic geometry. Investigate topics including Monge-Ampère type 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 a distinguished committee of mathematicians at the Instituto de Matemática Pura e Aplicada in Rio de Janeiro.