Algebra Algebra, Homological Algebraic geometry Algèbre Algèbre homologique Applications Combinatorial group theory Combinatorics Commutative algebra Cycles and subschemes Determinantal varieties Geometry Geometry, Algebraic Géométrie Géométrie algébrique Graph theory Homological functors on modules (Tor, Ext, etc.) Homological methods Linkage, complete intersections and determinantal ideals Parametrization (Chow and Hilbert schemes) Projective and enumerative geometry Projective techniques Special varieties Surfaces and higher-dimensional varieties Syzygies, resolutions, complexes Theory of modules and ideals Théorie combinatoire des groupes Vector bundles on surfaces and higher-dimensional varieties, and their moduli