Title: Asymptotic behavior of value semi-groups

Abstract: Let v be a valuation dominating a noetherian local domain, let S = {v(r) | r is in R} be its value semi-group and let G be its value group (the group obtained by appending inverses to S). The possible value groups G have been extensively studied and classified classically; the value semi-group S however is much less understood. In this talk we will briefly look at the known results classifying value groups and at some well known constraints on the value semi-groups. Then we will look at growth rate of the value semi-group and its asymptotic behavior to obtain new constraints on possible value semi-groups.

This is joint work with S. D. Cutkosky and O. Kashcheyeva.