"Interaction between fluids and structures motivated by real-life problems: micro-swimmers, vascular stents, and heart valves"

Department of Mathematics, University of Houston

Institute for Computational and Mathematical Engineering, Stanford University

## Abstract:

Real-life problems are an important driving force in the development of new mathematics. With the recent developments of new technologies, biomedical engineering and medicine, the need for new mathematical and numerical methodologies to aid these developments has never been greater. Real-life problems are oftentimes mathematically rich and very complex. Certain simplifications usually have to be taken into account to obtain a mathematically tracktable problem that captures the leading-order physics or physiology well. In this talk I will focus on problems motivated by biomedical applications that have for the past 25 years driven the development of mathematical theory and design of numerical methods in partial differential equations modeling the interaction between incompressible, viscous fluids such as blood, and structures, such as cardiovascular tissue, vascular prostheses called stents, or micro-swimmers used in drug delivery.