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This brings up a far-reaching open problem: given a closed manifold $\\Sigma^k$ with non-negative sectional curvature, which vector bundles over $\\Sigma$ admit complete metrics with non-negative curvature? In this talk we will talk about the history of this problem and answer a longstanding question of Grove-Ziller. We show that every vector bundle over every homotopy 7-sphere admits non-negative curvature. 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