|XXXV Workshop on Geometric Methods in Physics
Elliptic and Hyperelliptic Fibrations in Integrability
The integrability version of E. Wigner's famous pronouncement,
"The Unreasonable Effectiveness of Mathematics in the Natural Sciences," could be, "the unreasonable effectiveness of the addition law in achieving integration by quadratures". Behind it, is a powerful geometric structure of the parameter space of the equations of motion, namely an elliptic or hyperelliptic fibration. This talk will focus on a hyperelliptic model (Toda Lattice) and on an elliptic surface (difference-equation systems), highlighting a new link and proposing a bridge to mirror symmetry.