HITCHIN SYSTEMS: SOME RECENT ADVANCES

The uploaded paper is a survey that states the parabolic topological mirror symmetry and the precise congruence condition e ≡ λ d (mod Δ_P) (Def. 3.20 and Thm. 3.22), attributing the result to prior work and explicitly framing it via the GWZ p-adic integration method and the relation between gerbes and Tate duality; it also explains the Δ_P=1 simplification (Thm. 3.23) and the technical codimension issue and how it is handled in the parabolic setting . The candidate solution follows that same GWZ/Shen p-adic integration blueprint: spreading out, working fiberwise over the Hitchin base (supported by parabolic BNR/generic-fiber structure), matching twists via Tate duality and fiberwise Poisson summation, and then identifying p-adic volumes with stringy E-polynomials, with the same Δ_P congruence and Δ_P=1 consequence; these ingredients are all present or summarized in the paper’s survey sections and references . Minor nuance: the survey credits Su–Wang–Wen for the equality and notes Shen’s p-adic refinements, whereas the model’s outline leans on Shen’s parabolic p-adic argument; this is a referencing nuance, not a mathematical conflict.