CERAMATHS - DMATHS seminar: presentation by Youness Lamzouri

The CERAMATHS Mathematics Department seminar will welcome, exceptionally at 1pm, Youness LAMZOURI (Institut Élie Cartan, Nancy, and Institut Universitaire de France), on Thursday, January 25, 2024, for the following talk:

Class numbers of subfamilies of quadratic bodies

A fundamental problem in number theory is to calculate the number of classes of a number field K, an important quantity that measures the unique factorization defect in the ring of integers of K. The case of quadratic fields has a rich history, dating back to Gauss's work on binary quadratic forms. In the case of real quadratic bodies, there are very few results concerning the number of classes. In particular, a conjecture by Gauss dating from 1801 and still open to this day, states the existence of an infinite number of real quadratic bodies whose number of classes is 1. In this talk, we will review the history of this subject, and present results concerning large values of these class numbers, as well as applications.