Building swimming micro-robots, for medical purposes (for instance in order to do less invasive micro surgery) needs, besides a very miniaturized technology, a deep understanding of the swimming mechanisms in water at the micro scale. Many such mechanisms already exists in nature since e.g. bacteria or sperm cell use cilia, flagella or shape deformations in order to propel themselves in the fluid.
However, the physical regime in which those microorganisms live is totally different from the one that one encounters at a larger scale. Inertia is negligible and one needs to use the fluid viscosity for the propulsion. As a matter of comparison, this regime is the same for very viscous fluid flows, when the fluid is silicon, honey, paint, or even at a larger scale the flows seen in glaciers. The right model for this regime is given by Stokes equations which is a linear PDE.
The talk will give a tour among the mathematics associated to these questions. At the interface between biology, physics and mathematics, its mathematical study also requires knowledge in analysis, geometry, numerical analysis and control theory.