Here is a paper on differential forms, with a view towards defining de Rham cohomology. The target audience should know some algebra (definitions of groups, rings, vector spaces), topology (definitions of topological spaces, continuous maps and homeomorphisms), and multivariable real analysis (differentiable maps \( \mathbb{R}^n\to\mathbb{R}^m \) ).

Here is a paper on supersymmetry in enumerative geometry. In particular, the paper explores (very crudely) what a supersymmetric quantum field theory is, and shows how in one special case, it actually counts the critical points of a function. The target audience need not know any physics, but a previous encounter with the least action principle is helpful. At the end, some very basic complex analysis is used (definition and properties of holomorphic functions).

Here is a paper on a special case of conjectured log-concavity of the Whitney numbers of the second kind. All relevant definitions are included, so the prerequisites are extremely minimal.

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