Galois Theory: A branch of algebra that studies the symmetries of the roots of polynomials, particularly through the structure of Galois groups. Arboreal Galois Representations: ...

Differential Galois Theory: A field of study that examines the algebraic structure of differential equations by associating them with groups of symmetries. Algebraic Group: ...

For instance, the Galois group immediately tells you whether a polynomial can be solved at all, and it allows you to compare the underlying structure of different polynomials. Galois groups can also ...

To present an introduction to Galois theory in the context of arbitrary field extensions and apply it to a number of historically important mathematical problems. Unit Description. Consider a field, ...

MATH 8822 Number Theory II (Spring: 3) Possible topics include: Factorization of ideals, local fields, local-vs-global Galois theory, Brauer group, adèles and idèles, class field theory, Dirichlet ...