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Answers
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Discrete Morse theory and existence of minimal complex
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Triangulations of polytopes and tilings of zonotopes
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Representability of matroids over $\mathbb R$
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Prescribing areas of parallelograms (or 2x2 principal minors)
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What makes four dimensions special?
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Interesting conjectures “discovered” by computers and proved by humans?
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The category of posets
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What would you want to see at the Museum of Mathematics?