Detta Dickinson

*CANCELLED* The distribution of algebraic conjugate points in small boxes

A point (x_1,x_2,x_3) is an algebraic conjugate point if P(x_i)=0 for each i=1,2,3 where P is an integer polynomial. Consider the set of integer polynomials of height at most Q and degree at most n. There are (within constants) Q^{n+1} such polynomials and therefore Q^{n+1} triples of conjugate points. The aim of the talk is to show that in a small rectangular box J in [0,1]^3 the number of such triples is of the order of Q^{n+1}|J| (where |J| is the volume of the box). The methods used are from metric Diophantine approximation.