| Consider a space with a lattice of points in it, such as the integer points in Euclidean space. Now take a figure in the space and enlarge it by dilation: we want to count the lattice points inside the shape as it grows, as precisely as possible. This simple-sounding problem has many surprises-- for instance, it takes on a very different flavor depending on whether the sides of the shape are curvy or straight. The subject ties number theory to geometry by design, but I will import it to the setting of group theory as well. | ||
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