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Hydrodynamics plays a crucial role in many cellular processes. One example is the locomotion of cells such as bacteria, spermatozoa, and essentially half of the microorganisms on earth. These organisms typically possess flagella, slender whiplike appendages which are actuated in a periodic fashion in a fluid environment, thereby giving rise to propulsion. Motivated by recent experimental data, we consider in this talk three problems on the nonlinear hydrodynamics of swimming cells. We first address the observed flagellar synchronization between eukaryotic cells swimming in close proximity. We then explain why cells swimming in confined environments are attracted to nearby boundaries. We finally pose two optimization problems addressing the optimal geometry, and optimal gait of low-Reynolds number swimmers. Host: Konstantine Turitsyn |