Speaker: Matt Kahle
Title: Complicated configuration spaces
Abstract: We'll first discuss the configuration space of n points in the plane. This is an open manifold that is well studied and well understood, and we will start by reviewing its basic properties. On the other hand, if we replace the points with particles with some thickness, and replace the plane with some bounded region, not very much is known.
This would be nice to understand better. For example, various questions related to motion planning for robots can be formulated in terms of topology of these spaces. For another example, if the particles are disks, then the configuration space can be considered to be the "energy landscape" for a 2-dimensional hard spheres gas. Understanding more about the topology and geometry of such spaces would be very interesting from the point of view of physics.
Note: This is part of the Invitations to Mathematics lecture series given each year in Autumn and Spring semesters. Pre-candidacy students can sign up for this lecture series by registering for one or two credit hours of Math 6193, class #16988 (with Prof H. Moscovici).