8 May 2025. Talk by Roberto Rubio at the UIUC Symplectic and Poisson geometry seminar.
Abstract: Generalized complex geometry encompasses complex and symplectic structures. I will start by recalling this by using just differential forms. Other geometric structures, such as cosymplectic or almost contact, involve or can be reformulated also in terms of differential forms. However, they are defined on odd-dimensional manifolds, where generalized complex geometry cannot reach. I will then introduce a natural extension of generalized complex geometry to manifolds of any dimension, known as Bn-generalized complex geometry, and show their unifying power. 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.