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Tuesday, April 26, 2016

**Abstract:** It is a classical problem to determine which complex topological vector bundles on CP^n admit an algebraic structure. We will discuss ``obstructions" to equipping a bundle with an algebraic structure coming from A^1-homotopy theory (though I won't presuppose any knowledge of A^1-homotopy theory). The main goal of the talk is to analyze the question of whether some rank 2 bundles on CP^n constructed by Elmer Rees using homotopy theoretic techniques admit an algebraic structure. This talk is based on joint work with Jean Fasel and Mike Hopkins.