Abstract: After providing a mathematical background for some curious optical experiments in the 19th century, we will then describe how these ideas inform our understanding of the Deift conjecture for the Korteweg--de Vries equation. Specifically, they allow us to show that the evolution of almost-periodic initial data need not remain almost periodic. This colloquium-style talk is based on joint work with Andreia Chapouto and Monica Visan.
