This talk will focus on a new periodization scheme for boundary integral methods. The scheme will allow us to quickly and accurately solve the Stokes equations in geometrically complex domains. We will then extend the scheme to handle flows with deformable particles and will focus on several applications to microfluidics. For one such application, we were able to simulate over 1000 deformable vesicles flowing through a complex geometry, using a laptop, in less than one minute per time step. For another, we were able to discover a new microfluidic chip design that provided faster cell separation. Speaker(s): Gary Marple (University of Michigan)