Tell me about the Langlands program The Langlands program is a set of far-reaching conjectures in mathematics that connect number theory, representation theory, and harmonic analysis. It was proposed by the mathematician Robert Langlands in the 1960s and has since become one of the most influential and active areas of research in mathematics. At its core, the Langlands program seeks to establish deep connections between two seemingly unrelated branches of mathematics: number theory and representation theory. Number theory is concerned with the properties and relationships of whole numbers, while representation theory deals with abstract algebraic structures known as groups. The main idea behind the Langlands program is that there exists a correspondence between certain types of mathematical objects called automorphic forms (which arise from number theory) and representations of algebraic groups (which are studied in representation theory). This correspondence is known as the Langlands correspondence. The Langlands program has had a profound impact on various fields of mathematics. It has led to breakthroughs in number theory, algebraic geometry, and even theoretical physics. The program has provided new insights into classical problems such as Fermat's Last Theorem, the distribution of prime numbers, and the behavior of L-functions. Despite its wide-ranging influence, many aspects of the Langlands program remain conjectural or partially understood. The program has inspired numerous researchers to make significant contributions over several decades. Some parts have been proven in specific cases or for certain classes of objects, but a complete proof or formulation still eludes mathematicians. In recent years, efforts have been made to reformulate and refine the Langlands program using modern tools from geometry, topology, and mathematical physics. This ongoing research continues to deepen our understanding and uncover new connections between different areas of mathematics. Overall, the Langlands program represents a grand vision that seeks to unify diverse branches of mathematics through deep interconnections. Its far-reaching implications have made it a central area of study for mathematicians around the world. # References ```dataview Table title as Title, authors as Authors where contains(subject, "Langlands") sort title, authors, modified ```