Alexander Gaifullin Flexible polyhedra: Constructions, Volume, Scissors Congruence, Big Seminar

It is our pleasure to share the Big Seminar talk Flexible polyhedra: Constructions, Volume, Scissors Congruence by Alexander Gaifullin. Abstract: Flexible polyhedra are polyhedral surfaces with rigid faces and hinges at edges that admit nontrivial deformations, that is, deformations not induced by ambient isometries of the space. Main steps in theory of flexible polyhedra are: Bricards construction of selfintersecting flexible octahedra (1897), Connellys construction of flexors, i. e., nonselfintersecting flexible polyhedra (1977), and Sabitovs proof of the Bellows conjecture claiming that the volume of any flexible polyhedron remains constant during the flexion (1996). In my talk I will give a survey of these classical results and ideas behind them, as well as of several more recent results by the speaker, including the proof of Strong Bellows conjecture claiming that any flexible polyhedron in Euclidean threespace remains scissors congruent to itself during the flexion (joi