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 ...
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 ...
Proceedings of the American Mathematical Society, Vol. 144, No. 5 (May 2016), pp. 1931-1938 (8 pages) Abstract. We show that the Vojta (or Hall-Lang) conjecture implies that the arboreal Galois ...
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 ...
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