A-model on ruled surfaces

Duiliu-Emanuel Diaconescu (Rutgers University) spoke about a generalization of the topological vertex techniques to the case of a new type of Calabi-Yau spaces that do not have to be toric: namely bundles of ruled surfaces that still admit a toric action - one that becomes degenerate not at singular points but on curves.

He conjectured a formula for the A-model topological partition sum in terms of some recursion relations describing elementary building blocks of the base of the manifold. Cumrun Vafa argued that he had the final general answer in which the recursion relations are explicitly solved, and it has not been decided yet whether Cumrun's universal ultimate answer was correct. Unfortunately the topic is too math-intensive for this blog to tell you more details.