"This project aims at developing a theory of growth, dynamics and mechanics of bio-filaments including branching processes. It will then be applied to a variety of physically and biologically interesting systems.At the mathematical level, the growth of biological filaments involves interesting aspects of both kinematics and dynamics of curves. A natural starting point for the modeling of biofilaments is to consider them as thin elastic rods subjected to external constraints. The basic idea is to cross-sectionally average all stresses along the space curve representing the centreline of the rod. This leads to a set of equations, the Kirchhoff equations, relating averaged forces and moments to the curve’s strains (characterized by the curvatures, shears, and extension). These equations provide the starting point for much theoretical analysis and numerical modeling. They are valid for a large range of scales and have been used to model many different structures including DNA, vines and plants.Early work will be the basis for establishing a general and rigorous theory of growing elastic rods that we referred to as morphoelastic rods. Various microscopic mechanisms for the generation of intrinsic macroscopic curvature, torsion and twist will be studied. Furthermore, the initiation of branching points will be described. Simultaneously, we will consider various applications in life sciences to motivate these general theories. In particular, in collaboration with various biologists, we will model the growth of neurons and plants."