Hiroshi Nozaki Few distance sets and the Dodecahedron conjecture, Mo CCA20

The talk Fewdistance 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 sdistance set if the number of distances between two distinct points in X is equal to s. An sdistance set with large size sometimes has a good combinatorial structure like association schemes. A major problem for sdistance sets is to determine the largest possible sdistance set for given s and dimension. The dodecahedron conjecture is that the largest possible 5distance set in 3dimensional Euclidean space is the vertices of the regular dodecahedron, which was long standing open problem. In this talk, we introduce several results of sdistance 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