Speaker: Denis Koleda
19 August, 2020 13:30 UTC
Abstract: In the talk we consider the spatial distribution of points that have algebraic (Galois) conjugate coordinates of fixed degree and bounded height. We give an asymptotic formula for counting such points in a wide class of regions of Euclidean space (as the parameter that bounds heights grows to infinity). We explain connection of this formula to random polynomials with i.i.d. coefficients. We also discuss some corollaries and applications of the formula. The talk is based on a joint work with F. Götze and D. Zaporozhets.