By Tancredi Schettini Gherardini (Universität Bonn, Germany), guest of the HUN-REN Morphodynamics Research Group, delivered a lecture with the title
AI-assisted design of homogeneous mono-monostatic polyhedra
on 2nd Oct at 16:00 in room F11 of building F.
Abstract: In this talk, I present a mono-monostatic polyhedron, explicit and
certified. Lángi proved the existence of such bodies, and our
construction realises one as a simple polytope with 56946 facets.
Alongside the data, we provide a rigorous certificate that such rational
polytope has exactly one stable and one unstable equilibrium point, and
no saddle equilibria, with respect to its exact centre of mass. The
construction therefore turns the known existence result into a concrete,
independently verifiable finite object. Much of the coding concerning
optimisation, search and certification was performed by an AI agent, and
a main theme of the talk will be emphasising some interesting features
of this new workflow.