Pure Mathematics Seminar: Oleg Karpenkov

Oleg Karpenkov, University of Liverpool

Wednesday 20 November 2013, 1500-1600
A54, Postgraduate Statistics Centre Lecture Theatre

On finite and infinitesimal flexibility of discrete and semidiscrete surfaces

In this talk we discuss geometric, algebraic, and computational aspects of finite and infinitesimal flexibility of Kokotsakis meshes. A Kokotsakis mesh is a mesh that consists of a face in the middle and a certain band of faces attached to the middle face by its perimeter. In particular any (3 × 3)-mesh made of quadrangles is a Kokotsakis mesh.

We express the infinitesimal flexibility condition in terms of Ceva and Menelaus theorems. Further we study semi-algebraic properties of the set of flexible meshes and give equations describing it. For (3 × 3)-meshes we show flexibility conditions in terms of face angles. In conclusion we say a few words about semidiscrete case.