Galois Representation

A Galois representation is a mathematical tool that describes how a symmetry group—originating from equations' solutions—acts on algebraic structures like number fields. Think of it as a way to encode complex symmetries and transformations in a formal, structured manner, translating them into matrices or linear algebra objects. This helps mathematicians understand deep properties of equations and numbers, linking abstract symmetry concepts with more concrete algebraic data, and plays a vital role in areas like number theory and the proof of longstanding conjectures.