Migrating in a Curved Environment

The field of active matter is the result of applying statistical physics to the motion of biological and biomimetic systems, from animal flocks to the cell's cytoskeleton and from robotic swarms to self-propelled colloids. Unlike bird flocks, which can move around freely, cells inside an organism or filaments inside a cell move in a very confined space bounded by curved walls. What is more, the shape of the boundaries can affect the dynamics in dramatic ways. Recently my focus has been on building a theoretical framework to study such problems by combining the concepts of active matter with those of the geometry of curved surfaces. I will discuss what such an approach can teach us about the way active systems respond to the geometry of their environment and what I hope it can teach us about the way such systems deform their environment and regulate their own shape.