Hiroshi Nozaki - “Few-distance sets and the Dodecahedron conjecture“ | MoCCA’20

The talk “Few-distance sets and the Dodecahedron conjecture“ by Hiroshi Nozaki on the Moscow Conference on Combinatorics and Applications at MIPT. Annotation: A Euclidean subset X is called an s-distance set if the number of distances between two distinct points in X is equal to s. An s-distance set with large size sometimes has a good combinatorial structure like association schemes. A major problem for s-distance sets is to determine the largest possible s-distance set for given s and dimension. The dodecahedron conjecture is that the largest possible 5-distance set in 3-dimensional Euclidean space is the vertices of the regular dodecahedron, which was long standing open problem. In this talk, we introduce several results of s-distance sets relating algebraic combinatorics and show some properties for substructures of the regular dodecahedron to prove the dodecahedron conjecture. We also give only a sketch of the proof of the conjecture, the following speaker Dr. Shinohara will ex