My research is concerned with mathematical modeling and computer simulation for problems arising in biology and medicine. My principal research effort, beginning in my Ph.D. thesis, has been the mathematical modeling of blood flow in the heart with particular emphasis on the heart valves. From this work has emerged an original computational method for fluid-structure interaction that is now called the “immersed boundary method” (I don’t know who gave it this name!). A large part of my current work, and that of my students, involves the further development of this methodology. Its application to a growing list of ever more diverse and challenging applications includes a stochastic version for microscopic problems in which Brownian motion plays an important role. This is the regime in which biomolecular motors operate, which is another of my research interests. There is even an immersed boundary method for the bidomain equations of cardiac electrophysiology, which is an electrical rather than a mechanical problem. In the field of electrophysiology, I am also interested in modeling electrodiffusion as a means of studying the role of 3D microanatomy in neural science.