Substrate Geometry
Taking classical geometric primitives — the oloid, the Gömböc, mono-monostatic bodies — and iterating on them to improve real engineering substrates.
Computational rolling-contact mechanics that classifies shapes by physical invariants rather than by appearance: seven physics oracles, a 25.6× mean-temperature advantage on the TPMS heat-exchanger geometry, and a 58× improvement in contact distribution.
The programme produced the first openly verified Gömböc construction and a 13-member verified mono-monostatic catalog, both released with their computation rather than as a claim.
Paper I was endorsed on arXiv by Georg Nawratil (TU Vienna), after Hellmuth Stachel — who originated the oloid problem — read the work and referred it onward to him. The methodology paper is under review at the SMAI Journal of Computational Mathematics; the TPMS heat-exchanger paper is under review at Elsevier Results in Engineering.