Alex Küronya will speak on

Newton-Okounkov bodies and local positivity

Abstract: The concept of Newton-Okounkov bodies is a recent attempt to understand the asymptotics of vanishing behaviour of global sections of line bundles on projective varieties via convex geometry.
In this talk I first give a quick outline of the existing theory while the second part of the lecture will be devoted to a study of local positivity of ample line bundles via Okounkov bodies, a joint work with Victor Lozovanu.