For the polynomial x to the fourth plus three x squared plus five, it associates the dihedral group of order 8.
The Langlands program in mathematics relates to the attempt to understand this as applied to the algebraic closure of the rational numbers. For the polynomial x to the fourth plus three x squared plus five, it associates the dihedral group of order 8. It involves eponymous groups of automorphisms of a field that preserve a given subfield. The fundamental theorem of this subject establishes a one-to-one correspondence between subgroups of its namesake group and intermediate fields of a field extension. Although its most famous result was proved earlier by Abel, the establishment of this field led to a deeper understanding of the insolubility of the quintic equation by radicals. For 10 points, what is this branch of mathematics named for a French mathematician who was killed in a duel at age 20?
The Langlands program in mathematics relates to the attempt to understand this as applied to the algebraic closure of the rational numbers.
Galois theory