Ilia Zharkov, Kansas State University

Title: Perfect Necklaces.

Abstract: Given m white beads and n black beads what is the most perfect necklace can one make? A necklace is perfect if for any fixed k the number of black (or white) beads in consecutive k-strings varies at most by one. A short note by M. Kontsevich in the Russian Math/Psysics magazine for high school students "Kvant" 07/1985 claims that for any pair (n,m) the perfect necklace exists and is unique up to rotations. I will give several other interesting incarnations of perfect necklaces including the infinite ones.