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Explore the intricate relationship between holomorphic symplectic structures and elliptic fibrations in this mathematical lecture. Delve into the case where a complex surface X admits a nowhere vanishing holomorphic 2-form, which determines a holomorphic symplectic structure on X. Examine how the symplectic geometry relates to the underlying complex geometry of elliptic surfaces, focusing on the geometric properties that emerge from this interaction. Learn about recent research developments in this specialized area of complex geometry through work conducted in collaboration with Guolei Zhong. Gain insights into advanced topics in algebraic geometry, particularly the intersection of symplectic geometry and elliptic fibration theory. This presentation was recorded during the thematic meeting "Complex Geometry, Complex Analysis and Dynamics" at the Centre International de Rencontres Mathématiques in Marseille, France.
