Contact Info
Pure MathematicsUniversity of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada
N2L 3G1
Departmental office: MC 5304
Phone: 519 888 4567 x43484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
Igor Shparlinski, University of New South Wales
“Effective Hilbert’s Nullstellensatz and Finite Fields”
We give an overview of recent applications of effective versions of Hilbert’s Nullstellensatz to various problems in the theory of finite fields. In particular, we resent some results about the size of the set generated by s-fold products of some rational fractions in a finite field. This result has some algorithmic applications.
We also show that almost all points on algebraic varieties over finite fields avoid Cartesian products of small order groups. This result is a step towards Poonen’s conjecture.
We finish with an outline of some open problems.
MC 5479
Departmental office: MC 5304
Phone: 519 888 4567 x43484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.