We study the genus expansion of Barannikov-Kontsevich solutions of the WDVV equation. In terms of the related graph calculus, we give a definition of descendants at one point and prove that this definition satisfies the topological recursion relations in genera 0, 1, and 2, string and dilaton equations, and the pull-back formula.

The dimensional reduction of $D$-dimensional spacetimes arising in string/M-theory, to the conformal Einstein frame, may give rise to cosmologies with accelerated expansion. Through a complete analysis of thedynamics of doubly warped product spacetimes, in terms of scale invariant variables, it is demonstrated that for $D \geq$ 10, eternally accelerating four-dimensional $\kappa$ = - Friedmann cosmologies arise from dimensional reduction on an internal space with negative Einstein geometry.

BF theory is a topological theory that can be seen as a natural generalization of three-dimensional gravity to arbitrary dimensions. Here, we show that the coupling to point particles that is natural in three dimensions generalizes in a direct way to BF theory in $d$ dimensions coupled to $(d − 3)$-branes. In the resulting model, the connection is flat except along the membrane world-sheet, where it has a conical singularity whose strength is proportional to the membrane tension. As a step towards canonically quantizing these models, we show that a basis of kinematical states is given by “membrane spin networks”, which are spin networks equipped with extra data where their edges end on a brane.

We develop computational tools for the tree-level superpotential of B-branes in Calabi-Yau orientifolds. Our method is based on a systematic implementation of the orientifold projection in the geometric approach of Aspinwall and Katz. In the process, we lay down some ground rules for orientifold projections in the derived category.