RESUMEN: The purpose of this talk is to discuss the maximal possible (algebraic) intersection of closed curves of a given length on translation surfaces. One way to quantify this is to define the so-called “interaction strength” of the surface. The (moduli) space of translation surfaces comes with a natural SL(2,ℝ)-action and we are interested in understanding the behaviour of the interaction stength under this action.
After having introduced translation surfaces and the SL(2,ℝ)-action, we will give a few geometric ideas and focus on the case of the Golden L for which we can explicitely describe the behaviour of the interaction strength in the SL(2,ℝ)-orbit.