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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
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Complexity of detecting a convex body in $\mathbb{R}^n$?
Let $K_0$ be a bounded convex set in $\mathbb{R}^n$ within which lie two sets $K_1$ and $K_2$. $K_0,K_1,K_2$ have nonempty interior. Assume that,
$K_1\cup K_2=K_0$ and $K_1\cap K_2=\emptyset$.
The b …