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

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