Pure Math MS student Ryan Bridges will be defending his thesis on May 8, 2020, at 2 PM remotely through Zoom; if you wish to attend contact Janet for the Zoom credentials.

Lattice of Maximal-Primary Ideals in Quadratic Orders

An order is a subring of the ring of integers of an algebraic extension.  Peruginelli and Zanardo classified the lattices of orders of with prime index inside the ring of integers of quadratic extension of the rational numbers.  The lattices are quite striking and have different layered structure depending on whether the prime is inert, split or ramified.  Ryan's thesis considers the orders which have prime power index inside the Gaussian integers.  Ryan has obtained the lattice structure of the maximal-primary ideals for the maximal ideal which contains the conductor in the setting that the prime is inert.  This is a nice generalization of the work of Peruginelli and Zanardo.