• website

References (partly) indexed on the $n$Lab

• Higher Topos Theory (arXiv, published version)

  on higher category theory and higher topos theory

• (∞,2)-categories (arXiv)

  on higher category theory

• Stable ∞-Categories (arXiv)

  on stable homotopy theory and homological algebra

• Noncommutative Algebra (arXiv)

  and

  Commutative Algebra (arXiv)

  on higher algebra

  alert: the new version is now here

  the new version differs from the previous one by embedding the theory of symmetric monoidal (∞,1)-categories into a theory of (∞,1)-operads.

• Deformation Theory (arXiv)

  on the notions of Kähler differential and cotangent complex and their generalization from the ordinary context of algebra to that of higher algebra.

• Structured Spaces (arXiv)

  • on structured (∞,1)-toposes and generalized schemes

• On the Classification of Topological Field Theories (arXiv)

  on functorial extended topological quantum field theory

• A Survey of Elliptic Cohomology (pdf)

  on the generalized (Eilenberg-Steenrod) cohomology theory tmf, the gluing of all elliptic cohomology theories

• (∞,2)-Categories and the Goodwillie Calculus (pdf)

  on (∞,1)-categories of (∞,n)-categories and Goodwillie calculus

• $𝔼[k]$-Algebras (pdf)

  on little cubes (∞,1)-operads

Warning These documents keep being updated and expanded. On the personal webpage as well as, with the due time delay, on the arXiv. Likely many references to page and definition/theorem numbers on the $n$Lab to these articles are already outdated

• PhD thesis, derived algebraic geometry (pdf)

  on derived algebraic geometry

  all the material in there should now be, in more complete and more coherent form, in the articles above. But some papers will cite page and verse in the PhD thesis, so it is useful to have that as a reference, too.

• note on dg-Lie algebras as formal neighbourhoods of point in infinity-stacks.