Research Interests - David Brander
I am interested in problems in geometry in general, and also applications in architecture and
design.
Integrable Geometry
Most of the work I have published is on geometric problems that are represented
by special nonlinear partial differential equations called integrable systems.
These problems admit exact solutions by loop group techniques, a theory that has
its roots in the soliton theory that was developed from the 1960's onwards.
Problems that I have worked on using these methods include isometric immersions between
space forms and generalizations of these to reflective submanifolds, constant mean
and Gauss curvature surfaces in various space forms, Willmore surfaces and surfaces with
singularities. I have also implemented numerical methods for computing most of these surfaces.
There are a few
images here, with a little background on the
problems they relate to.
Geometry in Architecture
I am interested in applications of geometry in archictecture and design. The development of
new fabrication techniques results in the need for design and rationalization tools that allow
architects to take advantage of these techniques. This leads to interesting problems in geometry.
An example of this is the hot wire and hot blade fabrication technology development by
Odico, that I am involved in through the
projects
Bladerunner and
Digital Factory, funded by the
Danish Innovation Fund.
This work develops a new technique for cutting architectural formwork, intended to allow
the construction of advanced shapes much more efficiently than is currently possible.
Publications and Preprints