Title: Parametrizing Ideal Classes
Speaker: Melanie Wood
Speaker Info: Stanford
Special Note: The speaker will give an introductory talk for graduate students at 11 am in Lunt 104.
The parametrization of ideal classes of quadratic rings by integral binary quadratic forms has played an important role in number theory. We will discuss two directions in which this classical result can be generalized. We can parametrize ideal classes of quadratic extensions of some fixed number field K by binary quadratic forms (properly interpreted) over the ring of integers of K. We can also parametrize the class groups of some special rings in degree n number fields by classes of triple tensors. These parametrizations can be given concretely and also in the language of algebraic geometry.Date: Monday, November 29, 2010