This paper concerns open, closed, and open-closed topological conformal field theories. We show that the category of open topological conformal field theories, at all genera, is homotopy equivalent… (More)

[1] Magnetically active times, e.g., Kp > 5, are notoriously difficult to predict, precisely the times when such predictions are crucial to the space weather users. Taking advantage of the routinely… (More)

The modular envelope of a cyclic operad is the smallest modular operad containing it. A modular operad is constructed from moduli spaces of Riemann surfaces with boundary; this modular operad is… (More)

This paper gives a way to renormalise certain quantum field theories on compact manifolds. Examples include Yang-Mills theory (in dimension 4 only), Chern-Simons theory and holomorphic Chern-Simons… (More)

I prove a formula expressing the descendent genus g Gromov-Witten invariants of a projective variety X in terms of genus 0 invariants of its symmetric product stack S g+1 (X). When X is a point, the… (More)

This paper gives a construction, using heat kernels, of differential forms on the moduli space of metrised ribbon graphs, or equivalently on the moduli space of Riemann surfaces with boundary. The… (More)

This is the sequel to my preprint“TCFTs and Calabi-Yau categories”. Here we extend the results of that paper to construct, for certain Calabi-Yau A∞ categories, something playing the role of the… (More)

The ribbon graph decomposition of moduli space is a non-compact orbi-cell complex homeomorphic to Mg,n×R>0. This was introduced by Harer-Mumford-Thurston [Har86] and Penner [Pen87], and used to great… (More)