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Stanley Yao Xiao

I am currently a PHD Candidate in Pure Mathematics, University of Waterloo. I am being advised by Professor Cameron Stewart, FRSC. In Fall 2016 I will be starting a Research Fellow at the University of Oxford.

I am interested in analytic number theory, prime number theory, transcendence theory, and power-free values of polynomials. In particular I work on problems involving applications and generalizations of the determinant methods pioneered by Bombieri/Pila, Heath-Brown, and Salberger, including the real analytic determinant method, the approximate determinant method of Heath-Brown, and the global determinant method of Salberger (an extension of the $p$-adic determinant method of Heath-Brown), as well as other potential variants.

Recently, I have been doing work on binary forms and classical invariant theory. In particular, together with my advisor we found the asymptotic formula for the number of integers in an interval which can be represented by a given binary form $F$ of degree $d\geq 3$ with integer coefficients and non-zero discriminant.