Motivated by applications such as ink jet printing, drop-by-drop manufacturing, sprays, emulsions, and chemical separations, we study the dynamics of breakup and coalescence through high-accuracy simulation, theory, and experiment. In this talk, I will highlight our group's work on accurately capturing the fluid dynamics that takes place in the vicinity of finite-time singularities. The free surface flow algorithms and solvers that we develop and use rely on a sharp interface representation of phase boundaries. In the simulations, we are able to analyze situations that involve disparate length scales that differ by up to seven orders of magnitude (commercial codes can handle about 2-3 orders and custom codes can capture at most 3-4 orders of magnitude disparity in length scales). The primary focus of the talk will be on simulations of the breakup of surfactant covered filaments where I will pay special attention to the pinch-off singularity. I will also summarize some of our recent work on the pre- and post-coalescence singularities that arise when two drops or bubbles are driven together and made to merge into one. Speaker(s): Osman Basaran (Purdue University)