## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Monday, November 30, 2015 — 4:00 PM EST

**Xiaoheng Jerry Wang, Princeton University**

"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.

MC 5501

*Refreshments will be served in MC 5501 at 3:30 pm.
Everyone is welcome to attend.*

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1