Polytopes, Rings, and K-Theory

Winfried Bruns has contributed numerous articles to homological and combinatorial commutative algebra. The book Cohen-Macaulay Rings he co-wrote with J. Herzog has become a standard reference. His work in discrete convex geometry is presented in the book Polytopes, Rings and K-Theory co-authored with J. Gubeladze, and in the software package Normaliz. Aldo Conca has written over seventy papers in commutative algebra. His main contributions are related to determinantal rings, Gröbner degenerations, Koszul and quadratic algebras, and Koszul homology. More recently, he has been involved in projects where commutative algebra is applied to "real world" problems. Claudiu Raicu has contributed to the study of homological invariants in commutative algebra and algebraic geometry, with an emphasis on problems involving symmetries coming from a group action. In the case of determinantal varieties and schemes, his work includes explicit calculations of a number of invariants such as local cohomology groups, Lyubeznik numbers, Hodge ideals, Ext modules and asymptotic regularity. Matteo Varbaro has contributed to the study of various topics in commutative algebra. His contributions include results on Gröbner deformations, determinantal objects, local cohomology, combinatorial commutative algebra, F-singularities, Castelnuovo-Mumford regularity.