Yongqiang Zhao, Department of Pure Mathematics, University of Waterloo
“On sieve methods for varieties over finite fields"
Although sieve methods in classical analytic number theory have a long and very fruitful history, its appearance in algebraic geometry is relatively new, and was introduced by Bjorn Poonen about ten years ago. In this talk, we will first discuss Poonen’s sieve through a concrete example on counting degree d smooth homogeneous polynomials over finite fields, then we will introduce a new interpolation technique to sieve methods and use it to study the distribution of rational points of the moduli spaces of trigonal curves over finite fields.
The first half of the talk is for a general audience. In the first 20 minutes of this talk, neither knowledge of algebraic geometry nor sieve theory is assumed. All are welcome!