PROBLEMS AND PROGRESS IN MICROSWIMMING

Stokesian swimming is a geometric exercise, a collective game. In Part I, we review Shapere and Wilczek's gauge-theoretical approach for a s ingle organism. We estimate the speeds of organisms moving by propagat ing small amplitude waves, and we make a conjecture regarding a new in equality for the Stokes' curvature. In Part II, we extend the gauge th eory to collective motions. We advocate the influx of nonlinear contro l theory and subriemannian geometry. Computationally, parallel algorit hms are natural, each microorganism representing a separate processor. In the final section, open questions motivated by biology are present ed.