AbstractIn analogous to the Hodge theory, Tsai, Tseng and Yau constructed a novel cochain complex on symplectic manifolds, based on the Lefschetz decomposion. Its cohomology is closely related to the de Rham cohomology, but also carries the information of the symplectic form. In the talk we will go through the definition and properties of this cochain complex
Abstract: The equations of flux compactification of Type IIA superstrings were written down by Tomasiello and Tseng-Yau. To study these equations, we introduce a natural geometric flow known as the Type IIA flow on symplectic Calabi-Yau 6-manifolds. We prove the wellposedness of this flow and establish the basic estimates. We show that the Type IIA flow can be applied to find optimal almost com...