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Langlands Program

November 21, 2023

GS Paper III Science and Technology

Context:

The Langlands program provides a beautifully intricate set of connections between various areas of mathematics, pointing the way toward novel solutions for old problems.

What is Langlands program?

The Langlands program is named after Robert Langlands, a mathematician at the Institute for Advanced Study in Princeton.
- In 2018, he was awarded the Abel Prize, one of the most prestigious awards in mathematics, for his program, which was described as “visionary.”
This program was set in motion in 1967.
Program is an attempt to find connections between two far-flung areas of mathematics: number theory and harmonic analysis.
- Number theory: It 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: It 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).

News Source: The Hindu

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