= Jacob Lurie
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<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>.<On the Classification of Topological Field Theories by Jacob Lurie>[Abstract and introductory formulation]{ref}
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>.<Morava E-Theory and Morava K-Theory by Jacob Lurie>[Lecture 22, Definition 5]{ref}
\Image[https://www.ias.edu/sites/default/files/styles/portrait/public/images/scholars/3725-1704906312.jpg.webp?itok=u7GIg_7n]
{title=Jacob Lurie, Institute for Advanced Study portrait}
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