Langlands Program

November 24, 2023

This program was set in motion in 1967 by Dr. Robert Langlands at Princeton University.
Langlands Program consists of “very complicated theoretical abstractions, which can be difficult even for specialist mathematicians to grasp”.
At the heart of the Program is an attempt to find connections between two far-flung areas of mathematics: number theory and harmonic analysis.
- Number theory is the arithmetic study of numbers and the relationships between them.
  - A famous example of such a relationship is the Pythagoras theorem: a2 + b2 = c2.
- Harmonic analysis is interested in the study of periodic phenomena.
  - Unlike number theorists, who deal with discrete arithmetics (like integers), harmonic analysts deal with mathematical objects more continuous in nature (like waves).
- In 2018, Dr. Langlands was awarded the Abel Prize, one of the highest honours for mathematicians, for “his visionary program connecting representation theory to number theory”.