"Density of polynomials with squarefree discriminant"
The problem of the density of squarefree discriminant polynomials is an old one, being considered by many people, and the density being conjectured by Lenstra. A proof has been out of question for a
long time. The reason it was desired is that a squarefree discriminant polynomial f immediately gives the ring of integers of Q[x]=f(x); so it's useful to know that most of the time one can get directly at the ring of integers. In recent joint work with Manjul Bhargava and Arul Shankar, we counted the number of polynomials with squarefree discriminant and proved the conjecture of Lenstra. In this talk, I will explain the general strategy of the squarefree sieve and the speci c strategy to deal with
discriminant which in turn leads to counting integral orbits for a representation of a non-reductive group.
Everyone is welcome to attend.