Special Lecture: Crossing the cut: Approximation on multiple Riemann sheets

When a holomorphic function is analytically continued along two paths with the same endpoints, there is no guarantee they arrive at the same value. The natural domain resolving this is a Riemann surface, a multi-sheeted cover of the plane on which the function becomes single-valued, but in which the function’s quantities of interest like zeros and poles end up residing on sheets beyond the principal one where data is available. Motivated by this setting, this talk addresses whether an approximant built from sampled data on one sheet can serve as a proxy on multiple sheets simultaneously.