CCOR Workshop

The Corvinus Center for Operation Research (CCOR) invites you to the CCOR Workshop titled Searching for monostatic polyhedra with optimization.


Gábor Domokos (Budapest University of Technology and Economics)
Krisztina Regős (Budapest University of Technology and Economics)
Sándor Bozóki  (Institue for Computer Science and Control, Corvinus University of Budapest)
Dávid Papp (North Carolina State University, Non-resident research fellow at CIAS-CCOR)
Gergő Almádi (Budapest University of Technology and Economics)

Venue: Corvinus University, Building C, Room: C105

Date: January 19. (Friday), 11:00-13:15

Abstract: The stability of polyhedra was investigated first by Conway and Guy, and independently by Heppes in the 60s. A convex body is called mono-(un)stable if it has a unique (un)stable equilibrium. It is monostatic if it belongs to either of the two classes, and mono-monostatic, if it belongs to both. The Gömböc, constructed by Domokos and Várkonyi in 2006, is the first known mono-monostatic, homogeneous convex body. Several monostable polyhedra have also been found, but the minimal number of vertices (faces, edges) is unknown. Mono-unstability is even less understood; mono-monostatic homogenous polyhedra have not been explicitly constructed. Our four short talks will cover the geometry behind the stability of polyhedra; its algebraic reformulation into systems of polynomial inequalities; solvability of such systems using optimization techniques; and finally the inhomogenous case.