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In the earliest days of MathOverflow, there was a '20 questions' seminar (see <http://sbseminar.wordpress.com/category/20-questions/>) run by graduate students at Berkeley. Many questions from the sem…
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projective algebraic varieties endowed with an Abelian group structure. Over the complex numbers, they can be described as quotients of a vector space by a lattice of full rank. …
Arguments working entirely at a high level of abstraction, particularly category-theoretic arguments.
a poset satisfying a list of properties shared by face lattices of polytopes.
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
Questions on the subject additive combinatorics, also known as arithmetic combinatorics, such as questions on: additive bases, sum sets, inverse sum set theorems, sets with small doubling, Sidon sets,…
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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
the study of the geometry of Alexandrov spaces, which are non smooth analogues of Riemannian manifolds with curvature bounded from below.