{"id":"doi:10.5281/zenodo.23255347","kind":"article","title":"Geometric Langlands Conjecture Proved: A Grand Unified Theory Milestone — E8 Intelligence Research","authors":["Andrew Stewart Caldin"],"author_count":1,"year":2026,"published":"2026-10-09","venue":"Zenodo (CERN European Organization for Nuclear Research)","cited_by":0,"doi":"10.5281/zenodo.23255347","arxiv_id":null,"nct_id":null,"source_url":"https://doi.org/10.5281/zenodo.23255347","archive_url":"https://space-kitty.com/papers/doi:10.5281/zenodo.23255347","updated":null,"pmid":null,"pmcid":null,"openalex_id":"W7221121320","pdf_url":null,"abstract":"FINDING: Langlands program seeks a \"grand unified theory\" of mathematics linking number theory, harmonic analysis, and geometry; recent proof of the geometric Langlands conjecture is a major milestone. | MATH: Core objects are automorphic forms and Galois representations; the geometric Langlands correspondence is an equivalence of derived categories of D-modules on the moduli stack of G-bundles (Bun_G) and the derived category of quasi-coherent sheaves on the Langlands dual stack (Loc_{^L G}). Key dual group: ^L G (Langlands dual, e.g., SU(n) ↔ PSU(n)). No explicit numeric constants appear in the search results; the structure is categorical, not scalar. | CONNECTION: The Langlands dual group construction is rooted in root systems (Dynkin diagrams) — the same Lie-theoretic data underlying crystallographic root systems and Weyl groups. The moduli stack Bun_G and its dual Loc_{^L G} encode symmetries analogous to lattice dualities (e.g., weight lattice ↔ coweight lattice). The p-adic cate Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com","abstract_license":"CC-BY (publisher license, via OpenAlex)","license":"cc-by","is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Advanced Algebra and Geometry"],"details":null,"provenance":"openalex","attribution":"Abstract of \"Geometric Langlands Conjecture Proved: A Grand Unified Theory Milestone — E8 Intelligence Research\" by Andrew Stewart Caldin, https://doi.org/10.5281/zenodo.23255347, used under its Creative Commons Attribution license (CC-BY); markup removed, otherwise unmodified.","topics":[{"slug":"landmark-math-results","name":"Landmark Results in Pure Mathematics","domain_slug":"math-cs"}],"cited_in_dossiers":[]}