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

• Linear Batalin-Vilkovisky quantization as a functor of ∞-categories (with Owen Gwilliam)
  • Selecta Mathematica 24(2) (2018), 1247-1313 (doi:10.1007/s00029-018-0396-0)
  • arXiv:1608.01290 (3 Aug 2016)
• Two models for the homotopy theory of ∞-operads (with Hongyi Chu and Gijs Heuts)
  • Journal of Topology 11(4) (2018), 856-872 (doi:10.1112/topo.12071)
  • arXiv:1606.03826 (13 June 2016)
• Iterated spans and classical topological field theories
  • Mathematische Zeitschrift 289(3) (2018), 1427-1488 (doi:10.1007/s00209-017-2005-x)
  • arXiv:1409.0837 (29 Nov 2018; includes a correction to the published version)
• Lax colimits and free fibrations in ∞-categories (with David Gepner and Thomas Nikolaus)
  • Documenta Mathematica 22 (2017), 1225–1266
  • arXiv:1501.02161 (2 Jun 2015)
• On the equivalence between Θ_n-spaces and iterated Segal spaces
  • Proceedings of the AMS 146 (2018), no. 4, 1401–1415 (doi:10.1090/proc/13695)
  • arXiv:1604.08480 (28 Apr 2016)
• The higher Morita category of E_n-algebras
  • Geometry and Topology 21-3 (2017), 1631-1730 (doi:10.2140/gt.2017.21.1631)
  • arXiv:1412.8459 (20 May 2016)
• On a spectral sequence for the cohomology of infinite loop spaces (with Haynes Miller)
  • Algebraic and Geometric Topology 16-5 (2016) 2911-2947 (doi:10.2140/agt.2016.16.2911)
  • arXiv:1302.1816 (19 Jul 2015)
• Bimodules and natural transformations for enriched ∞-categories
  • Homology, Homotopy and Applications 18 (2016) 71-98 (doi:10.4310/HHA.2016.v18.n1.a5)
  • PDF (13 Aug 2015), arXiv:1506.07341 (24 Jun 2015)
• Rectification of enriched ∞-categories
  • Algebraic and Geometric Topology 15-4 (2015) 1931-1982 (doi:10.2140/agt.2015.15.1931)
  • arXiv:1312.3881 (2 Jun 2015)
• Enriched ∞-categories via non-symmetric ∞-operads (with David Gepner)
  • Advances in Mathematics 279 (2015) 575–716 (doi:10.1016/j.aim.2015.02.007)
  • arXiv:1312.3178 (12 Jan 2015)

Preprints

• Homotopy-coherent algebra via Segal conditions (with Hongyi Chu)
  • arXiv:1907.03977 (9 Jul 2019)
• Shifted coisotropic correspondences (with Valerio Melani and Pavel Safronov)
  • arXiv:1904.11312 (25 Apr 2019)
• Segal spaces, spans, and semicategories
  • arXiv:1901.08264 (24 Jan 2019)
• ∞-operads as analytic monads (with David Gepner and Joachim Kock)
  • arXiv:1712.06469 (18 Dec 2017)
• ∞-operads via symmetric sequences
  • arXiv:1708.09632 (31 Aug 2017)
• Enriched ∞-operads (with Hongyi Chu)
  • arXiv:1707.08049 (25 Jul 2017)

Talk Slides

• Topological quantum field theories and higher algebraic structures
  • Norwegian National Mathematicians' Meeting, 14 September 2018
• Enriched (∞,n)-Categories and TQFTs
  • 15 minute presentation in MPIM Oberseminar, 17 July 2014
• Spectral Sequences for the Cohomology of Finite and Infinite Loop Spaces
  • Young Topologists' Meeting, 30 June 2014

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.