News excerpt:
Langlands Program is the World's Largest Math Project Connecting Number Theory and Harmonic Analysis.
About:
- Robert Langlands, awarded the Abel Prize in 2018, initiated the Langlands Program in 1967, connecting representation theory to number theory.
- Langlands Program aims to find connections between number theory (study of numbers) and harmonic analysis (study of periodic phenomena).
- It bridges the gap between discrete arithmetic (numbers like integers) and continuous mathematical objects (like waves).
- The Program explores symmetries in polynomial equations through Galois groups and connects them to automorphic functions using tools from calculus.
- Langlands Program has evolved into its own field, including Geometric Langlands, exploring connections with algebraic geometry and even physics.
Significance of Programme:
- Andrew Wiles and Richard Taylor (The British mathematicians) used Langlands' conjectures to prove Fermat's final theorem in 1994. For more than three centuries, mathematicians have been unable to find this proof.
- The Program has also assisted mathematicians in creating new automorphic functions from existing ones. They recognise that such possibilities could be critical in proving the Ramanujan conjectures, many of which remain unanswered.
