Stanley Xiao, Department of Pure Mathematics, University of Waterloo
“Rational automorphisms of binary quartic forms”
Last week, we saw that there is a canonical correspondence between binary quartic forms and elliptic curves which preserves the I and J invariants of the form. Bhargava and Shankar showed using this correspondence that the PGL2(Q) automorphism group of integral binary quartic forms are isomorphic to the rational-2-torsion subgroup of the corresponding elliptic curve. In this talk, we will generalize the theorem of Bhargava and Shankar and give a full classification of possible automorphism groups of integral binary quartic forms with non-zero discriminant in the larger group GL2(Q).
MC 5479