Khovanskii's Theorem and Effective Results on Sumset Structure

A remarkable theorem due to Khovanskii asserts that for any finite subset $A$ of an abelian group, the cardinality of the $h$-fold sumset $hA$ grows like a polynomial for all sufficiently large $h.$ However, neither the polynomial nor what sufficiently large means are understood in general. I will describe recent work (joint with Michael Curran, Oxford) in which we obtain an effective version of Khovanskii's theorem for any subset of $Z^d$ whose convex hull is a simplex; previously such results were only available for $d=1.$ Our approach also gives information about the structure of $hA,$ answering a recent question posed by Granville and Shakan.
Conference ID: 942 0186 5629 Password is a six-digit number, the first three digits of which form the number p + 44, and the last three digits are the number q + 63, where p, q is the largest pair of twin primes less than 1000