The packing problem of multidimensional balls

Recently (March 2016) a young Ukrainian mathematician, Maryna Viazovska (Мари́на Сергíївна В'язо́вська) have found the maximal density of packing of congruent balls in the eight-dimensional Euclidean space. Soon, a group of authors, including Maryna Viazovska, solved the similar problem in the space of dimension 24, by using methods modelled on the preceding work of Maryna. In the talk we will present the main ideas of this work and related beautiful mathematical structures.