a (1+1)-dimensional topological quantum field theory is a tensor functor from the category of 2-dimensional cobordisms to the category of vector spaces. it is easy to give a characterisation of such functors: they are determined by the vector space associated to a single circle together with the structure maps it inherits from the disc and the pair of pants, which make it into a finite-dimensional frobenius algebra. a (1+1)-dimensional conformal field theory is a much more subtle thing, being a functor from the category of riemann surfaces (2-dimensional cobordisms equipped with complex structures or "moduli") to a category of hilbert spaces. somewhere between lies the idea of topological conformal field theory, which is a "chain level" version of a cft. it is determined by a chain complex on which the spaces of chains of the (morphism spaces of the) category of riemann surfaces act. such a structure arises in several places in modern topology, most notably in the theory of gromov-witten invariants of symplectic manifolds and in the sullivan-chas string topology of a loop space. this term we aim to read kevin costello's paper "topological conformal field theories and calabi-yau categories" (math.qa/0412149), which gives an algebraic characterisation of tcfts analogous to the "frobenius algebra" classification of tqfts. in the first talk in the series i will try to give an overview of what the paper says, and we will organise talks for the rest of the term.