The Gromov-Hausdorff distance between two metric spaces is an important tool in geometry, but it is difficult to compute. For example, the Gromov-Hausdorff distance between unit spheres of different dimensions is unknown in nearly all cases. I will introduce recent work by Lim, Mémoli, and Smith that finds the exact Gromov-Hausdorff distances be...
Creator:
Adams, Henry (Colorado State University)
Created:
2022-08-04
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Suppose ball-shaped sensors wander in a bounded domain. A sensor doesn't know its location but does know when it overlaps a nearby sensor. We say that an evasion path exists in this sensor network if a moving intruder can avoid detection. Vin de Silva and Robert Ghrist give a necessary condition, depending only on the time-varying connectivity d...
Creator:
Adams, Henry (University of Minnesota, Twin Cities)
Created:
2014-03-05
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Consider a Vietoris-Rips complex of the circle with the geodesic metric. This simplicial complex has an infinite number of vertices, one for each point in the circle. A theorem of Jean-Claude Hausmann implies that for small connectivity parameter, the Vietoris-Rips complex is homotopy equivalent to a circle. What happens as the connectivity para...
Creator:
Adams, Henry (University of Minnesota, Twin Cities)
Created:
2014-05-06
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Consider the Vietoris-Rips complex for n evenly-spaced points around a circle. For small choices of the connectivity parameter, this complex is homotopy equivalent to a circle. For n even and for a connectivity parameter slightly less than the diameter of the circle, this complex is the boundary of a cross-polytope and is homeomorphic to the (n/...
Creator:
Adams, Henry (University of Minnesota, Twin Cities)
Created:
2013-10-01
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.