Generalising classical questions about regular polygons with vertices on a plane lattice, we are interested in pairs of points $A,B$ on a lattice such 
that the angle $hat{AOB}$ is a rational multiple of $pi$. This problem leads to diophantine-trigonometric equations that in turn involve the study of rational points on curves of genus 0,1,2,3,5. I will present the full classification of plane lattices according to how many independent rational angles they contain and in which configurations they appear. This is a joint work with R. Dvornicich, D. Lombardo and U. Zannier
org: Turchet Amos