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I have added to the beginning of the category:people entry Jacob Lurie a little bit of actual text. Please feel invited to further expand and fine-tune. Right now it reads as follows:
After an early interest in formal logic (see Notices of the AMS vol 43, Number 7) Lurie indicated in his PhD thesis how the moduli stack of elliptic curves together with the collection of elliptic cohomology spectra associated to each elliptic curve is naturally understood as a geometric object in a homotopy theoretic refinement of algebraic geometry that has come to be known as derived algebraic geometry. He then embarked on a monumental work laying out detailed foundations of the subjects necessary for this statement, which is homotopy theory in its modern incarnations as higher category theory, higher geometry in terms of higher topos theory and finally higher algebra in terms of higher operads, all in principle very much along the lines originally developed by Alexander Grothendieck and his school for ordinary algebraic geometry, but now considerably further refined to the general context of homotopy theory. While some developments in these topics had been available before, Lurie’s comprehensive work has arguably led these subjects to an era of reinvigorated activity with a variety of further spin-offs. Among these most notable is maybe the formalization and proof of the cobordism hypothesis, which lays higher monoidal category theoretic foundations for (local, topological) quantum field theory.
Added a smidgen to the first sentence.
Lurie is now a MacArthur Genius. http://www.macfound.org/fellows/921/.
I have added a reference subsection at Jacob Lurie containing the record of 4 references Lurie (co)authored 1999-2003 before he jumped fully into the new subject of derived algebraic geometry (before his thesis).
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