Friday, November 20th at 10:30, Matteo Gallet (SISSA, Trieste).

Title: Zero-sum cycles in flexible polyhedra
Abstract:  We show that if a polyhedron in the three-dimensional affine space with triangular faces is flexible, i.e., can be continuously deformed preserving the shape of its faces, then there is a cycle of edges whose lengths sum up to zero once suitably weighted by 1 and -1. We do this via elementary combinatorial considerations, made possible by a well-known compactification of the three-dimensional affine space as a quadric in the four-dimensional projective space. The compactification is related to the Euclidean metric, and allows us to use a simple degeneration technique that reduces the problem to its one-dimensional analogue, which is trivial to solve. This is a joint work with G. Grasegger, J. Legerský, and J. Schicho.

The seminar will take place online. Click here for the Zoom link.