Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMar 11th 2014
    • (edited Mar 11th 2014)

    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.

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeMar 11th 2014

    Added a smidgen to the first sentence.

    • CommentRowNumber3.
    • CommentAuthortrent
    • CommentTimeSep 20th 2014

    Lurie is now a MacArthur Genius. http://www.macfound.org/fellows/921/.

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeApr 13th 2016

    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).

  1. Removed broken link to picture.

    Ramkumar Ramachandra

    diff, v44, current

    • CommentRowNumber6.
    • CommentAuthorDavid_Corfield
    • CommentTimeApr 18th 2019

    Added in the Elliptic cohomology series. Part III has some orbispace/equivariant theory which may have something to say to the work here on equivariant cohesion.

    diff, v46, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeApr 19th 2019

    Thanks for the alert. In that case, should have the reference cited accordingly here, here and here :-)

    • CommentRowNumber8.
    • CommentAuthorDmitri Pavlov
    • CommentTimeApr 6th 2020

    Added a redirect.

    diff, v49, current