The work of Pavlov on shift operators on a Riemann surface

Boris Pavlov’s mathematical quest was centered on the interplay between operator theory, complex analysis, and mathematical physics. More specifically, he had an amazing vision relating the spectral analysis of an operator to nontrivial phenomena in function theory and to relevant properties of associated physical systems. The bilateral shift, its restriction the unilateral shift, compressions thereof to coinvariant subspaces, and vector-valued versions of all these, where of course central players in the story.