nLab Daniel Murfet

Daniel Murfet is an algebraic geometer; his PhD advisor was Amnon Neeman. Daniel keeps a blog The Rising Sea which is not very active, but hosts lots of (nice and reliable) Daniel’s expositional notes (pdf files) on algebraic geometry, homological algebra and some category theory.

• gScholar profile

Selected writings

On Grothendieck universes in category theory:

• Daniel Murfet, Foundations for category theory (2006) [pdf, pdf]

On machine learning:

• S. Wei, Daniel Murfet, M. Gong, H. Li , J. Gell-Redman, T. Quella, Deep learning is singular, and that’s good, IEEE Transactions on neural networks and learning systems pdf

On a category of matrix factorizations in the context of Landau-Ginzburg models, described in terms of linear logic and the geometry of interactions:

• Daniel Murfet, The cut operation on matrix factorisations, Journal of Pure and Applied Algebra

  222 7 (2018) 1911-1955 [arXiv:1402.4541, doi:10.1016/j.jpaa.2017.08.014]

Introduction to linear logic with amplification of its categorical semantics via linear algebra (in Vect/FinDimVect):

• Daniel Murfet, Logic and linear algebra: an introduction [arXiv:1407.2650]

On a bicategory of Landau-Ginzburg models with matrix factorizations as 1-morphisms:

• Nils Carqueville, Daniel Murfet, Adjunctions and defects in Landau-Ginzburg models, Advances in Mathematics 289 (2016) 480-566 [doi:10.1016/j.aim.2015.03.033, arXiv:1208.1481]

A bicategory of Landau-Ginzburg models where matrix factorizations supply morphisms is studied in

• Nils Carqueville, Daniel Murfet, Adjunctions and defects in Landau-Ginzburg models, Advances in Mathematics 289 (2016) 480–566 doi