Class Groups, Forms, and Arithmetic Statistics
OTHER MATHEMATICS DEPARTMENT EVENTS: MATH TABLE
When: April 16, 2025
4:30 pm - 5:30 pm
Where: Science Center 507
Address:
1 Oxford Street, Cambridge, MA 02138, United States
Speaker: Eliot Hodges - Harvard
The ideal class group of a number field F measures the extent to which the integral elements of F fail to factor uniquely into primes. Of central importance in number theory, ideal class groups were first studied by Gauss under the guise of binary quadratic forms. From this perspective, multiplication of ideals corresponds to Gauss’s celebrated composition law. In this talk, we develop Gauss’s theory of binary quadratic forms and discuss its arithmetic reinterpretation. We then present a modern reinterpretation of Gauss composition à la Bhargava and give an overview of many astounding arithmetic-statistical consequences of this theory.
For more information, visit the Math Table website.