Problems in geometry arising from architecture

Recent advances in construction methods and materials have led to the possibility of building structures of a more interesting geometrical nature than in the past, and thus an interest among architects and engineers in certain problems in the theory of surfaces.

In turn, the practicalities lead to new problems and methods in geometry.

Examples:

• The study of discrete surfaces constructed from quadrilateral nets
• The off-setting problem where a double layer consisting of two surfaces separated by a given distance is wanted

The practicalities can also lead to renewed interest in some classical problems. 

Examples:

• The study of isothermic surfaces (related to quadrilateral nets)
• The  classical Bjorling problem of minimal surfaces, which, more generally, is the problem of constructing a special type of surface which contains a given curve and with the tangent planes prescribed along this curve: this is related to the problem of smoothly matching two surfaces along a boundary

The department has the resources to support either a surface theoretical or a more computational project.

Contact person: David Brander