Jacob Lurie is a mathematician whose work develops higher category theory and its applications to algebraic geometry and homotopy theory. His 2009 paper sketches a proof of the cobordism hypothesis, a classification of extended topological quantum field theories.[ref]
On the Classification of Topological Field Theories by Jacob Lurie. Abstract and introductory formulation
The organizing idea is that the value on a point, with the appropriate duality properties, can determine the field theory on higher-dimensional manifolds and their cobordisms. Cutting and gluing become composition laws in a higher category. This explains why passing from whole manifolds to pieces of every dimension changes the algebraic framework. His chromatic lecture notes give another bridge between algebra and topology, constructing Morava K-theory from structured topological spectra.[ref]
Jacob Lurie, Institute for Advanced Study portrait
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Jacob Lurie is a prominent American mathematician known for his work in higher category theory, algebraic topology, and derived algebraic geometry. He has made significant contributions to the fields of homotopy theory and the foundations of mathematics, particularly through his development of concepts such as ∞-categories and model categories. Lurie is also known for his influential books, including "Higher Topos Theory" and "Derived Algebraic Geometry.