{"paper":{"title":"Mirror Symmetry, Hitchin's Equations, And Langlands Duality","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RT","authors_text":"Edward Witten","submitted_at":"2008-02-07T16:11:53Z","abstract_excerpt":"Geometric Langlands duality can be understood from statements of mirror symmetry that can be formulated in purely topological terms for an oriented two-manifold $C$. But understanding these statements is extremely difficult without picking a complex structure on $C$ and using Hitchin's equations. We sketch the essential statements both for the ``unramified'' case that $C$ is a compact oriented two-manifold without boundary, and the ``ramified'' case that one allows punctures. We also give a few indications of why a more precise description requires a starting point in four-dimensional gauge th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.0999","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}