Physicists working in String Theory have several conjectures regarding closed geodesics on Calabi-Yau manifolds. Motivated by these, I have recently been constructing closed geodesics in the K3 surfaces constructed by Lorenzo Foscolo. For these, it is possible to locate several closed geodesics with high precision and compute their index (their length is also approximately known)

Interestingly, the construction of these geodesics is related to an open problem in electrostatics posed by Maxwell in 1873.