| Speaker: John Guckenheimer Affiliation: Cornell University Time: 2 pm Wednesday, 20 February, 2019 Location: 303-310 |
| Curvature of curves and surfaces embedded in three space is a classic topic in undergraduate mathematics courses. This talk will discuss two computational aspects of the subject (1) Curvature of trajectories of vector fields and their dynamical significance, and (2) Computing the principal foliations of embedded surfaces by their lines of curvature. "Ridges" of the principal foliations are curves formed by local extrema of curvature along the lines of curvature. Their defining equations involve third derivatives, but computer representations of surfaces are seldom that smooth. The underlying issue of data structures for smooth manifolds will be touched upon. |