Chennai Mathematical Institute


3:30 pm, Seminar Hall
On the density of polynomials having squarefree discriminants

Arul Shankar
University of Toronto.


Consider the space of degree-n polynomials ordered by the sizes of their coefficients. A classical question in analytic number theory is: what proportion of them have squarefree discriminant? In this talk, I will discuss joint work with Bhargava and Wang in which we use methods from arithmetic invariant theory to determine this density. If time permits, I will describe an application, which is joint work with Ho and Varma, towards constructing families of number fields in which a positive proportion have odd class number.