Talk by Assistant professor Niels Martin Møller, Department of Mathematical Sciences, KU.
Abstract: I will start with the geometric background and differential
equations for some optimal shapes. Their dynamical versions which
seek to deform curves in the plane, or hypersurfaces in Euclidean
space (resp. abstract spaces), towards minimal length or area (resp.
constant curvatures) are then discussed. This can be (and has been)
used to answer some outstanding questions about the nature of
geometric spaces in various contexts.
In general, however, such an approach quickly meets the issue of
singularities (solitons) forming, which prevents the process from continuing.
This is an aspect closely connected to general notions of minimal surfaces.
Here I will also mention some of my own recent work regarding
what such singularities can (and cannot possibly) look like.
In working with this subject, many well-known (partial) differential
equations from elementary classical electromagnetism and from
quantum physics show up. I will explain all the material using
plenty of pictures and other illustrations.
Everybody is welcome!
Contact: Steen Markvorsen, stema@dtu.dk