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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. …
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Arguments working entirely at a high level of abstraction, particularly category-theoretic arguments.
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a poset satisfying a list of properties shared by face lattices of polytopes.
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Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
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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.
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For questions about $A_\infty$-algebras as introduced by Stasheff in 1963 and related structures.
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the study of the geometry of Alexandrov spaces, which are non smooth analogues of Riemannian manifolds with curvature bounded from below.
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