Arithmetic dynamics investigates the behaviour of iterated functions—often polynomials or rational maps—over number fields and function fields, while Galois theory provides the framework to analyse ...

Differential Galois theory extends the classical study of algebraic symmetries into the realm of differential equations. This area investigates the relationship between a differential equation’s ...

The quantum dimensions of modules for vertex operator algebras are defined and their properties are discussed. The possible values of the quantum dimensions are obtained for rational vertex operator ...

Transactions of the American Mathematical Society, Vol. 359, No. 2 (Feb., 2007), pp. 827-857 (31 pages) We discuss some of the basic ideas of Galois theory for commutative S-algebras originally ...

The Math 8806-8807 sequence will cover the following topics: Group Theory (Group actions, Sylow, Nilpotent/Solvable, simple groups, Jordan-Holder series, presentations); commutative algebra ...