6:00 PM-7:00 PM
Room: Rio Mar 5
Chair: Gilbert Strang, SIAM President, and Massachusetts Institute of Technology, USA
Propagating interfaces occur in a wide variety of settings, and include ocean waves, burning flames, and material boundaries. Less obvious boundaries are equally mportant, and include iso-intensity contours in images, handwritten characters, and shapes against boundaries. In addition, problems not thought of as moving interface problems often can be recast as advancing fronts, including finding robotic navigation and finding shortest paths on contorted surfaces.
One way to frame moving interface problems is by casting theme as solutions to partial differential equations, and this has led to Fast Marching Methods and Level Set Methods. There are some advantages to this view; in particular, they easily accommodate merging boundaries, problems in three dimensions, and very subtle motions of boundaries. In many settings, they been proven valuable.
The speaker will try to provide an overview of these approaches, with a focus on applications as well as new, murky applications, including the seemingly mystical question of how to "find boundaries that aren't there, while avoiding ones that are.''James A. Sethian