The Langlands Program

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Reciprocity Between Automorphic and Galois Data Beyond Known Cases

core

Compatibility of Arithmetic, Geometric, and Categorical Langlands Frameworks

core

Langlands Functoriality as a Universal Organizing Principle

core

Endoscopic Classification for Quasi-Split Classical Groups

supporting

Geometric Realization of Local Langlands via the Fargues--Scholze Framework

core

Class Field Theory

supporting

Global Langlands Correspondence for Function Fields and Reductive Groups

core

Global Langlands Correspondence for Reductive Groups over Number Fields

core

Principle of Functoriality

core

Construction of Galois Representations from Regular Algebraic Cuspidal Automorphic Representations of $GL_n$

supporting

Modularity of Elliptic Curves over $\mathbb{Q}$

supporting

Local Langlands Correspondence for $GL_n$

supporting

Global Langlands for $GL_n$ over Function Fields

supporting

Stabilization and Comparison of Trace Formulas

core

Local Langlands Correspondence for General Reductive Groups

core

Satake Isomorphism

supporting

Base Change and Automorphic Induction for $GL_n$

supporting

Fundamental Lemma

supporting

Categorical Geometric Langlands Equivalence

core

Betti and de Rham Geometric Langlands Correspondence

core

Geometric Langlands for $GL_n$ in Foundational Cases

supporting

Ngo's Support Theorem and the Hitchin Fibration

supporting

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