From blood flow to subsurface flows, particulate flows are ubiquitous. Direct numerical simulations of dense particle suspensions in viscous fluids, governed by Stokes equations, are extremely challenging yet critically important to bring insights into their macro-scale flow behavior. We will give an overview of research conducted by current (and past) graduate students in our department that helped overcome several computational bottlenecks in these problems using tools from complex analysis, potential theory, PDEs and numerical analysis. We will discuss how these methods can be useful in the design of microfluidic chips, shape optimization and in understanding the complex physics of soft particulate flows. Speaker(s): Shravan Veerapaneni (Michigan)