Modelling, control and analysis for micro-swimmers

Swimming strategies at the microscopic scale involve different mechanisms to those at the human scale. At this scale, the flow is dominated by the viscosity effects of the water and becomes reversible. This feature, known as the scallop theorem needs to be circumvented in order to swim with strokes that produce a net motion of the swimmer. The talk proposes to give an overview of recent works on this topic by the author and collaborators [1-7]. In particular, we will show how these problems sit at the intersection between fluid mechanics, control theory, theory of PDE and geometry.