Stanley Xiao, Department of Pure Mathematics, University of Waterloo
“A few facts that shocked a Fields Medalist: Some curious facts about binary quartic forms with small Galois group”
In this talk we discuss several curiosities of binary quartic forms whose Galois group is isomorphic to a subgroup of D4, the dihedral group of order 8. In particular, we will show that nearly all such quartic forms have non-square-free discriminant, that their J-invariants are reducible in a natural sense, and that most of them fail to even be locally soluble everywhere. When I conversed with Fields Medalist Manjul Bhargava on these topics, he found them shocking and genuinely thought the opposite was true in these instances.
MC 5403