**GTA Seminar | Speaker:** Ahmed Elshafei (CMAT)

**Title:** On the application of mathematics in architecture (Architectural Geometry)

**Abstract: **Architectural geometry is relatively new field of interdisciplinary research focusing on the application of differential geometry, topology, discrete-computational geometry, as well as mathematical physics in the process of architectural design and manufacturing.

In this talk, we will illustrate some examples of such applications, in particular of differential geometry and of integrable systems. We will show the crucial role that, certain curves networks (parameterizations) on surfaces, together with transformations leaving them invariant, play in architectural fabrication. Moreover, we also show some connections between local surface theory and integrable equations arising in mathematical physics, and how these can have useful applications in architecture. A classical example, is the sine-Gordon equation with its Bäcklund transformation and its connection to surfaces of constant negative curvature.