I will attempt to give a friendly introduction to the theory of $\infty$-operads, a powerful framework for working with homotopy-coherent algebraic structures. In the first talk I will introduce Lurie’s model of $\infty$-operads, and in the second I will survey some other models, including extensions to enriched $\infty$-operads.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/10159