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Jun 24, 2022 at 1:07 vote accept Anton Hilado
Jun 23, 2022 at 21:36 comment added David Ben-Zvi Thanks for the great answer! A purely linguistic comment: while of course you're right about boundary conditions, in physics language I think I'd say ramification data and Hecke operators correspond to surface and line operators (or codimension 2 and codimension 1 defects) in the theory, while codimension 1 defects (boundary conditions and interfaces / "domain walls") arise from things like periods and Langlands functoriality.
Jun 23, 2022 at 20:30 history answered Will Sawin CC BY-SA 4.0