Controlled Shape Growth in Biology

Living organisms come in an immense variety of shapes, such as roots, branches, leaves, and owers in plants, or bones in animals. For higher living forms, growing into the right shape is essential for survival. In some cases, Nature has found ways to control growth in an amazingly precise way.

From a mathematical perspective, this leads to some basic questions:

• (Q1) Can some of these shapes be recovered as solutions to optimization problems, in the spirit of the classical Calculus of Variations? What are the utility functionals and the constraints?
• (Q2) Can we describe a mechanism of controlled growth, which can eventually yield these optimal shapes?
• (Q3) Can one find some simple systems of PDEs, describing the shapes found in nature?

The ongoing research seeks to provide some partial answers, relying on analytical as well as computational tools.