Algebra

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Understanding symmetry, and how and why it arises in nature, is important in both Mathematics and Physics. Within my work the best examples are to be found in the connections between Algebraic Groups and Physics that have the Affine Kac-Moody Lie algebras as a common bridge. The mathematical objects that measure symmetry are called Groups. Lie groups, named after the Norwegian mathematician Sophus Lie who discovered and first studied these objects late in the 19th century, arise naturally as the underlying symmetry of many theories in Physics. The mid 20th century saw the birth of Algebraic Groups, objects that capture the spirit of Lie groups yet are much more universal. The research project centres on understanding the very nature of algebraic groups themselves, and their applications to several areas of Mathematics, as well as Physics.