Joint IAS/PU Number Theory

We propose and study a new arithmetic invariant of non-hyperelliptic genus-4 curves: a canonical “quadratic” point on the Jacobian, defined by the two natural degree-2 maps to projective lines. Building on Xue’s result, that this point is...

We will discuss an inductive approach to determining the asymptotic number of G-extensions of a number field with bounded discriminant, and outline the proof of Malle's conjecture in numerous new cases. This talk will include discussions of several...