Algebra, Homological

Combinatorial group theory

Geometry, Algebraic

Algebraic geometry > Cycles and subschemes > Parametrization (Chow and Hilbert schemes)

Algebraic geometry > Projective and enumerative geometry > Projective techniques.

Algebraic geometry > Special varieties > Determinantal varieties.

Algebraic geometry > Surfaces and higher-dimensional varieties > Vector bundles on surfaces and higher-dimensional varieties, and their moduli.

Combinatorics > Graph theory > Applications.

Commutative algebra > Homological methods > Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series.

Commutative algebra > Homological methods > Homological functors on modules (Tor, Ext, etc.)

Commutative algebra > Homological methods > Syzygies, resolutions, complexes.

Commutative algebra > Theory of modules and ideals > Linkage, complete intersections and determinantal ideals.