Iwasawa N Groups. Semisimple Lie groups and related objects are important in mathematics, theoretical physics (e.g., quantum mechanics and string theory), theoretical computer science (e.g., construction of expanders), and many other areas. They may be studied from different points of view---algebraic, analytic, geometric and representation theoretic---and these different studies find different applications. The project aims to synthesize the different points of view, to understand their funda ....Iwasawa N Groups. Semisimple Lie groups and related objects are important in mathematics, theoretical physics (e.g., quantum mechanics and string theory), theoretical computer science (e.g., construction of expanders), and many other areas. They may be studied from different points of view---algebraic, analytic, geometric and representation theoretic---and these different studies find different applications. The project aims to synthesize the different points of view, to understand their fundamental unity, and to allow results of one type to be translated into another context.Read moreRead less
Equivalence Relations, Group Actions, and Descriptive Set Theory. This project is a contribution to basic and foundational research in the area of Pure Mathematics generally and Mathematical Logic specifically. Logic in particular appears in disciplines as diverse as Computer Science,Linguistics, and Philosophy, and the development of logic in these fields has been profoundly influenced by the foundational work of mathematical logicians. The innovative techniques introduced in this proposal will ....Equivalence Relations, Group Actions, and Descriptive Set Theory. This project is a contribution to basic and foundational research in the area of Pure Mathematics generally and Mathematical Logic specifically. Logic in particular appears in disciplines as diverse as Computer Science,Linguistics, and Philosophy, and the development of logic in these fields has been profoundly influenced by the foundational work of mathematical logicians. The innovative techniques introduced in this proposal will enable Australia to maintain a position at the forefront of Pure Mathematics, and by recruiting a recent winner of the highly prestigious Karp prize the country will be instantly established as one of the leading centers of Mathematical Logic.Read moreRead less