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Geometry-Topology Seminar

Thursday, April 4, 2024 - 3:30pm

Thomas Brazelton



University of Pennsylvania


A fundamental question in algebra is to study and attempt to classify projective modules over a suitably nice ring. Following Serre, a fruitful direction of research is to import intuition from the topological study of vector bundles to make conjectures and prove statements about modules in algebra - a prime example being Quillen and Suslin’s resolution of Serre’s problem. Topological obstruction theory is a fundamental tool used in the study of vector bundles, and its motivic analogue can be wielded carefully in many settings to prove broad statements about algebraic vector bundles. In this mostly expository talk we will give a survey of recent developments in the theory of motivic obstruction theory, and their applications to the classification of algebraic vector bundles.