Simon Larson: Optimal stretching in lattice point problems

I will discuss some recent results in the realm of lattice point problems. Essentially the problem we will focus on can be thought of as choosing the optimal shape for the tiles when tiling your bathroom floor, in the limit when the size of the tiles goes to zero. As we don't want our floor to look too extravagant we stick to rectangular tiles, which reduces the problem to finding the best ratio between the sides.
This type of problem recently appeared in connection to asymptotic shape optimization in spectral theory, and has seen a drastic increase in interest during the past two years.