Geometric Representation Theory is a branch of mathematics that studies how algebraic structures, like groups and algebras, can be represented through geometric objects. It connects abstract algebra with geometry, allowing mathematicians to visualize and understand complex algebraic concepts using shapes and spaces. This theory often involves the use of manifolds and varieties, which are geometric structures that can represent solutions to algebraic equations. By exploring these connections, researchers can gain insights into the properties of Lie groups and representation theory, leading to advancements in both mathematics and theoretical physics.