Table of Contents

The Cone of Betti diagrams of bigraded Artinian modules of codimension.
Koszul cycles.
Boij-Söderberg Theory.
Powers of componentwise linear ideals.
Modules with 1-dimensional Socle and components of Lusztig Quiver varieties in Type A.
Realization spaces for tropical fans.
A relation between symmetric polynomials and the algebra of classes, motivated by equivariant Schubert Calculus.
Theory and applications of lattice point methods for binomial ideals.
Equations defining secant varieties: geometry and computation.