8 Apr 2025. Talk by Roberto Rubio at the IMPA Differential Geometry seminar.
Abstract: Many geometric structures such as symplectic, complex, cosymplectic, almost contact… involve or can be reformulated using differential forms. First, I will describe how generalized complex geometry uses this fact to encompass complex and symplectic geometry and show how much further it can get, always within even dimensions. I will then introduce a natural extension to manifolds of any dimension, known as Bn-generalized complex geometry. Finally, I will focus on the case of 3-manifolds, which is recent joint work with Joan Porti, shows novel phenomena and hints at an intriguing interaction between geometry and topology.