Describing minimal generating sets of toric ideals is a well-studied and difficult problem. Neil White conjectured in 1980 that the toric ideal associated to a matroid is generated...
It is proved that in R3 the volume of any polyhedron is a root of some polynomial with coefficients depending only on the combinatorial structure and the metric of the polyhedron....
Canetti, Goldreich, Goldwasser, and Micali (STOC 2000) introduced the notion of resettable zeroknowledge proofs, where the protocol must be zero-knowledge even if a cheating veri...
The rigidity of squares of graphs in three-space has important applications to the study of flexibility in molecules. The Molecular Conjecture, posed in 1984 by T-S. Tay and W. Wh...
Mathematics is facing a dilemma at its heart: the nature of mathematical proof. We have known since Church and Turing independently showed that mathematical provability was undeci...