Multiple translational tiling in the plane

In this talk, I will present some of my results in multiple translational tiling
in the Euclidean plane. For examples, besides parallelograms and centrally symmetric
hexagons, there is no other convex domain which can form any two-, three- or four-fold
translative tiling in the plane. However, there are two types of octagons and one type
of decagons which can form nontrivial five-fold translative tilings. Furthermore, a
convex domain can form a five-fold translative tiling of the plane if and only if it
can form a five-fold lattice tiling, a multiple translational tile in the plane is a
multiple lattice tile. This talk is based on a joint work with Professor Chuanming Zong.