Mathematical theory of quasicrystals

Quasicrystals are nonperiodic configurations in space that have many properties of crystals (i.e., periodic configurations). An example is the famous Penrose's tiling discovered in 1973. These objects attracted attention of mathematicians and physicists. In 1984, physicists obtained quasicrystallic metallic alloys with 5th order symmetry which is forbidden for crystals. Very soon mathematicians discovered remarkable connections between quasicrystals and harmonic analysis, mathematical physics, number theory, mathematical logic, dynamical systems. Some aspects of this theory is the subject of the lecture.