Representations of arithmetic groups and their associated zeta functions

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This project aims to investigate deep connections between number theory and group theory by studying linear actions of arithmetic groups. Arithmetic groups are used in geometry, dynamics, number theory and other areas of pure mathematics. This project will study their representations from two perspectives. First, it will establish properties of the associated zeta functions to resolve open problems about the asymptotic behaviour of the dimensions of the irreducible representations. Second, it will explore the evolution of representations across families of groups under new induction and restriction functors, in analogy with creation and annihilation operators in physics. The project will enhance Australia's capacity in representation theory and group theory, the mathematics that underline symmetry in nature.