Combinatorics and Algebraic Geometry have enjoyed a fruitful interplay since the nineteenth
century. Classical interactions include invariant theory theta functions and enumerative
geometry. The aim of this volume is to introduce recent developments in combinatorial algebraic
geometry and to approach algebraic geometry with a view towards applications such as tensor
calculus and algebraic statistics. A common theme is the study of algebraic varieties endowed
with a rich combinatorial structure. Relevant techniques include polyhedral geometry free
resolutions multilinear algebra projective duality and compactifications.
