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By Jacob Lurie.

Verified locator: Lecture 20, Definition 2, Example 4 and Example 7; universal property and rational localization.

By Jacob Lurie.

Verified locator: Sections 1.1–1.2: overview and language of higher categories. Published front matter identifies Princeton University Press, 2009.

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]

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]

By Jacob Lurie.

Verified locator: Abstract and introduction: proof sketch of the cobordism hypothesis and classification of extended field theories.

By Jacob Lurie.

Verified locator: Author course landing page; Lecture 1, Introduction, dated 3 February 2009, people.math.harvard.edu/~lurie/937notes/937Lecture1.pdf . Opening manifold classification and surface genus example; later lectures compare topological, PL and smooth structures.