Many fundamental phenomena in eukaryotic cells - nuclear migration, spindle positioning, chromosome segregation - involve the interaction of (often transitory) cellular structures with boundaries and fluids. Understanding the consequences of these interactions require specialized numerical methods for their large-scale simulation, as well as mathematical modeling and analysis. In this context, I will discuss the recent interactions of mathematical modeling and large-scale, detailed simulations with experimental measurements of activity-driven biomechanical processes within the cell. Speaker(s): Michael Shelley (New York University/Flatiron Institute)