■ Block 01 / research
Research
Foundations other work depends on. Each entry explains what it is, why it is load-bearing, its open problems, and a reviewed timeline of progress.
Foundations other work depends on. Each entry explains what it is, why it is load-bearing, its open problems, and a reviewed timeline of progress.
How densely can equal balls be packed in ℝ^d? Solved in dimensions 1, 2, 3, 8 and 24; elsewhere open, with large gaps between bounds, and tied to error-correcting codes and lattice cryptography.
The study of solution sets of polynomial equations and of the topology they carry; Hodge theory splits that topology into pieces that tell algebraic cycles apart from merely topological ones.