Optimal Flood Control

A mathematical model for optimal control of the water levels in a chain of reservoirs is studied. Some remarks regarding sensitivity with respect to the time horizon, terminal cost and forecast of inflow are made

Open rr-spin theory II: The analogue of Witten's conjecture for rr-spin disks

We conclude the construction of $r$-spin theory in genus zero for Riemann surfaces with boundary. In particular, we define open $r$-spin intersection numbers, and we prove that their generating function is closely related to the wave function of the $r$th Gelfand--Dickey integrable hierarchy. This provides an analogue of Witten's $r$-spin conjecture in the open setting and a first step toward the construction of an open version of Fan--Jarvis--Ruan--Witten theory. As an unexpected consequence, we establish a mysterious relationship between open $r$-spin theory and an extension of Witten's closed theory.Comment: The more foundational parts of the previous version, v3, were moved to the article arXiv:2003.01082. These include the description of objects, constructions of moduli spaces and bundles and proofs of orientations theorems. The name of the paper and the abstract were changed accordingl