Shapes on a plane: mechanical properties of geometric models of tissue

What governs the motion of cells inside an organism, or the collective mechanical properties of cells composing a tissue? The mechanical and dynamical properties of dense biological matter – e.g., whether it can support stresses, or whether it has surface tension – are obviously important for its biological function, but how can we coarse grain from the properties of single cells to try to understand the rich variety of collective behavior seen in these “living materials?” In this talk, I will discuss a theoretical framework for understanding dense cellular matter that coarse grains complex biological units into entirely geometric entities. I will also discuss how this family of geometrical models are different from alternative coarse-graining apporaches, focusing on the unusual structure of these models and the unique predictions they make for the behavior of real dense biological tissues.