Table of Contents

Newton-Okounkov Bodies of Exceptional Curve Plane Valuations non-Positive at Infinity.- Sufficient Conditions for the Finite Generation of Valuation Semigroups.- From Convex Geometry of Certain Valuations to Positivity Aspects in Algebraic Geometry.- Non-Positive at Infinity Valuations.- Very General Monomial Valuations on P2 and a Nagata Type Conjecture.- Valuations on Equicharacteristic Complete Noetherian Local Domains.- Desingularization by char(X)-Alterations.- Semigroup and Poincaré Series for Divisorial Valuations.- Computing Multiplier Ideals in Smooth Surfaces.- Notes On Divisors Computing MLD's and LCT's.- On the Containment Hierarchy for Simplicial Ideals.- The Universal Zeta Function for Curve Singularities and its Relation with Global Zeta Functions.- Algebraic Volumes of Divisors.- On Hirzebruch Type Inequalities and Applications.- On the Completion of Normal Toric Schemes over Rank One Valuation Rings.- Duality on Value Semigroups.- Notes on Local Positivity and Newton-Okounkov Bodies.- Newton-Okounkov Bodies and Reified Valuations of Higher Rank.