From infinity-categories to infinity-operads

In the last few decades higher category theory has not only become indispensable in the modern category-theoretic study of algebraic topology, but has also inspired and influenced many other areas of mathematics such as homological algebra and algebraic geometry or mathematical physics. During the course of these developments, it has become rather usual to have multiple models for higher categorical objects such as $(\infty,1)$-categories and $(\infty,1)$-operads. Each of these models usually has distinct advantages and it is often possible to move between different models via comparison results. In this talk I will first introduce simplicial categories and quasi-categories as two important approaches to $(\infty,1)$-categories and mention their comparison provided by a work of Cisinski and Moerdijk. We will then see how these concepts naturally generalize to simplicial operads and dendroidal sets, which model $(\infty,1)$-operads.