Arithmetic and algebraic aspects of the dynamics of polynomial semigroups

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This project aims to advance research in arithmetic dynamics, a rapidly developing field of mathematics that is rich in significant applications including cryptography. It will systematically study the semigroup action of several maps on an arithmetic space. The expected outcomes will extend existing concepts and theory, but also explore new mathematical phenomena related to number theory, graph theory and regular and chaotic arithmetic dynamics. There are likely applications in cryptography arising from the project and opportunities to build links between academia and national offices of information security.