Abstracts for IMPRS seminar on various topics: Homotopy algebras

Last time we introduced $L_\infty$-algebras and explained how they generalize Lie algebras. Even before their formal definition, $L_\infty$-algebras appeared in disguise as Sullivan's minimal models for rational homotopy types. In this talk, we will show that for every algebra $X$ over $\Omega C$, the cobar construction on some augmented cooperad $C$, we can produce an explicit minimal model, i.e.