Martin Doubek

Title: Open/closed string theory and operads [pdf]
Abstract: Worldsheets of open and closed strings form a modular operad QOC, which is easy to understand but still governs notrivial structures. First, QOC generalizes operads for cyclic associative and commutative algebras. This gives an alternative approach to characterization of open and closed topological field theories via Frobenius algebras. Second, a Feynman tranform of QOC governs algebras which generalize A-infinity and L-infinity algebras to their quantum counterparts. This structure is equivalent to solutions of Zwiebach's master equation in string field theory. It is also closely related to calculation of homology of the moduli space of complex curves. During the lecture, we will briefly explain these connections.