Research

I am interested in homotopy theory and higher category theory, and related areas such as derived (algebraic) geometry and (topological) quantum field theories.

Some Current Projects

  • The AKSZ construction in derived algebraic geometry as an extended TQFT (with Damien Calaque and Claudia Scheimbauer)
  • The higher Morita category of enriched (∞,n)-categories
  • Linear Batalin-Vilkovisky quantization as a functor of (∞,n)-categories (with Owen Gwilliam)
  • Enriched homotopy-coherent structures (with Hongyi Chu)
  • The universal property of bispans (with Elden Elmanto)

Publications

Preprints

  • Homotopy-coherent algebra via Segal conditions (with Hongyi Chu)
  • Shifted coisotropic correspondences (with Valerio Melani and Pavel Safronov)
  • Segal spaces, spans, and semicategories
  • ∞-operads as analytic monads (with David Gepner and Joachim Kock)
  • ∞-operads via Day convolution
  • Enriched ∞-operads (with Hongyi Chu)

Talk Slides

Thesis

  • Weakly Enriched Higher Categories (30 Apr 2013)
    • Warning: This contains a number of non-trivial errors. In any case, essentially everything in here can now be found in a much nicer and (as far as I know) correct form among the papers above.