Stanley Yao Xiao, Pure Mathematics, University of Waterloo
"Some results on binary forms and counting rational points on algebraic varieties"
In this talk we give an overview of the main results of my doctoral thesis. In particular, we discuss our result on establishing an asymptotic formula for the number of integers of bounded size which can be represented by a binary form (joint work with C.L. Stewart), the explicit determination of the automorphism group over any subfield of $\mathbb{C}$ of binary cubic and quartic forms under substitution action, our generalization of the global determinant method to the setting of weighted projective spaces, and applications of the $p$-adic determinant method to the problem of estimating power-free values of binary forms and the density of rational points on del Pezzo surfaces of degree 2.