Join us in welcoming OR’s own David Papp from the NC State Department of Mathematics as he discusses monostatic polyhedrons. Alums and friends of the program are always welcome.
https://ncsu.zoom.us/j/97198402775?pwd=dGN3ZDdldm1obXNXMTEzUkJlcElLdz09
Meeting ID: 971 9840 2775
Passcode: 557407
Searching for Monostatic Polyhedra: Computer-assisted Theorem Proving with Convex Optimization
The seminar concerns an unusual application of operations research: the stability of convex polyhedra, a fundamental question in 3-dimensional geometry whose study goes back to the 1960s. 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. Such convex bodies are surprisingly difficult to construct: 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) such a polyhedron must have is unknown. Mono-instability is even less understood; mono-monostatic homogenous polyhedra have not been explicitly constructed. In this seminar we will show not only how we can use optimization to construct mono-unstable polyhedra (the less surprising application), but also how to rigorously prove the non-existence of such polyhedra with few vertices. The talk will not assume any prior familiarity with the subject, only standard OR 505 material.
Dávid Papp is an associate professor in the Department of Mathematics at NC State. After studying at the Budapest University of Technology and Economics in Hungary, he obtained his Ph.D. in operations research at Rutgers University in 2011. Before joining NC State, he worked at Northwestern University and at the Massachusetts General Hospital. His research focuses on the design, analysis, and implementation of algorithms for solving large-scale optimization problems and their applications in healthcare, engineering, and statistics. His radiotherapy optimization algorithms are built into two clinical treatment planning software used worldwide (Philips Pinnacle and RaySearch RayStation). He received an NSF CAREER Award in 2019 for his computational mathematics research and the Mehrotra Award from the INFORMS Health Applications Society in 2021 for his work on radiation therapy.
