Dr Daniel Stevenson

Research Interests

Pure Mathematics

Dr Daniel Stevenson

Senior Lecturer

School of Mathematical Sciences

College of Science

My research interests lie at the interface of category theory and homotopy theory; I am especially interested in the interaction of ∞-categories with abstract homotopy theory.

My research interests lie at the interface of category theory and homotopy theory; I am especially interested in the interaction between the theory of ∞-categories and abstract homotopy theory. 

Date Position Institution name
2013 - ongoing Senior Lecturer University of Adelaide
2008 - 2013 Lecturer University of Glasgow
2007 - 2008 Research Associate University of Hamburg
2004 - 2007 Visiting Assistant Professor University of California, Riverside

Date Institution name Country Title
2000 University of Adelaide Australia PhD
1996 University of Adelaide Australia BSc Hons I

Year Citation
2025 Stevenson, D. (2025). A remark on the total simplicial set functor. Applied Categorical Structures, 33(3).
DOI
2023 Baez, J. C., Crans, A. S., Schreiber, U., & Stevenson, D. (2023). ERRATUM TO “FROM LOOP GROUPS TO 2-GROUPS”. Homology, Homotopy and Applications, 25(2), 403-405.
DOI
2020 Becker, K. E., Murray, M. K., & Stevenson, D. (2020). The Weyl map and bundle gerbes. Journal of Geometry and Physics, 149, 103572-1-103572-19.
DOI Scopus1 WoS1
2018 Stevenson, D. (2018). Model Structures for Correspondences and Bifibrations.
2018 Stevenson, D. (2018). Notes on the Joyal model structure.
2018 Stevenson, D. (2018). Stability for inner fibrations revisited. Theory and Applications of Categories, 33, 523-536.
Scopus2
2017 Stevenson, D. (2017). Covariant model structures and simplicial localization. North-Western European Journal of Mathematics, 3, 141-202.
2017 Murray, M., Roberts, D., Stevenson, D., & Vozzo, R. (2017). Equivariant bundle gerbes. Advances in Theoretical and Mathematical Physics, 21(4), 921-975.
DOI Scopus6 WoS7
2016 Roberts, D., & Stevenson, D. (2016). Simplicial principal bundles in parametrized spaces. New York Journal of Mathematics, 22, 405-440.
Scopus4 WoS1
2015 Nikolaus, T., Schreiber, U., & Stevenson, D. (2015). Principal $$\infty $$ ∞ -bundles: presentations. Journal of Homotopy and Related Structures, 10(3), 565-622.
DOI Scopus22
2015 Nikolaus, T., Schreiber, U., & Stevenson, D. (2015). Principal ∞-bundles: general theory. Journal of Homotopy and Related Structures, 10(4), 749-801.
DOI Scopus58
2013 Hekmati, P., Murray, M., Stevenson, D., & Vozzo, R. (2013). The Faddeev-Mickelsson-Shatashvili anomaly and lifting bundle gerbes. Communications in Mathematical Physics, 319(2), 379-393.
DOI Scopus1 WoS1
2012 Murray, M., Roberts, D., & Stevenson, D. (2012). On the existence of bibundles. Proceedings of the London Mathematical Society, 105(6), 1290-1314.
DOI Scopus3 WoS3
2012 Stevenson, D. (2012). Décalage and Kan's simplicial loop group functor. Theory and Applications of Categories, 26(28), 768-787.
Scopus11
2011 Murray, M., & Stevenson, D. (2011). A note on bundle gerbes and infinite-dimensionality. Journal of the Australian Mathematical Society, 90(1), 81-92.
DOI Scopus4 WoS4
2010 Stevenson, D. (2010). Geometry of infinite dimensional Grassmannians and the Mickelsson-Rajeev cocycle. Journal of Geometry and Physics, 60(4), 664-677.
DOI Scopus2
2008 Murray, M., & Stevenson, D. (2008). The basic bundle gerbe on unitary groups. Journal of Geometry and Physics, 58(11), 1571-1590.
DOI Scopus12 WoS11
2007 Varghese, M., & Stevenson, D. (2007). Entire cyclic homology of stable continuous trace algebras. Bulletin of the London Mathematical Society, 39(1), 71-75.
DOI Scopus4 WoS4
2007 Baez, J. C., Stevenson, D., Crans, A. S., & Schreiber, U. (2007). From loop groups to 2-groups. Homology Homotopy and Applications, 9(2), 101-135.
DOI Scopus87
2006 Varghese, M., & Stevenson, D. (2006). On a generalised Connes-Hochschild-Kostant-Rosenberg theorem. Advances in Mathematics, 200(2), 303-335.
DOI Scopus18 WoS20
2005 Carey, A., Johnson, S., Murray, M., Stevenson, D., & Wang, B. (2005). Bundle gerbes for Chern-Simons and Wess-Zumino-Witten theories. Communications in Mathematical Physics, 259(3), 577-613.
DOI Scopus65 WoS63
2004 Stevenson, D. (2004). Bundle 2-gerbes. Proceedings of the London Mathematical Society, 88(2), 405-435.
DOI Scopus29
2003 Varghese, M., Murray, M., & Stevenson, D. (2003). Type-1 D-branes in an H-flux and twisted KO-theory. The Journal of High Energy Physics, 11(11), www 1-www 22.
DOI Scopus9 WoS9
2003 Murray, M., & Stevenson, D. (2003). Higgs fields, bundle gerbes and string structures. Communications in Mathematical Physics, 243(3), 541-555.
DOI Scopus33 WoS31
2003 Varghese, M., & Stevenson, D. (2003). Chern character in twisted K-theory: Equivariant and holomorphic cases. Communications in Mathematical Physics, 236(1), 161-186.
DOI Scopus38 WoS39
2002 Bouwknegt, P., Carey, A., Varghese, M., Murray, M., & Stevenson, D. (2002). Twisted K-theory and K-theory of bundle gerbes. Communications in Mathematical Physics, 228(1), 17-45.
DOI Scopus149 WoS145
2000 Murray, M., & Stevenson, D. (2000). Bundle gerbes: stable isomorphism and local theory. Journal of the London Mathematical Society, 62(3), 925-937.
DOI Scopus83 WoS85

Year Citation
2009 Baez, J., & Stevenson, D. (2009). The classifying space of a topological 2-group. In T. N. M. Society (Ed.), Unknown Book (pp. 1-32). Heidelberg: Springer.
Scopus25

Year Citation
2000 Stevenson, D. (2000). The Geometry of Bundle Gerbes.

Year Citation
2012 Stevenson, D. (2012). Classifying theory for simplicial parametrized groups.

Date Role Research Topic Program Degree Type Student Load Student Name
2025 Principal Supervisor Higher classifying spaces Master of Philosophy Master Full Time Mr Alex Lewis Marciano
2025 Principal Supervisor Higher classifying spaces Master of Philosophy Master Full Time Mr Alex Lewis Marciano

Date Role Research Topic Program Degree Type Student Load Student Name
2023 - 2025 Principal Supervisor Classifying Spaces and Simplicial Groupoids Master of Philosophy Master Full Time Mr Matthew James Drown
2020 - 2022 Principal Supervisor Equivariant Bundle Gerbes and Simplicial Extensions Master of Philosophy Master Full Time Mr Liam Karl Stoldt
2019 - 2021 Principal Supervisor The Classifying Spaces of Some Categories Master of Philosophy Master Full Time Mr Kieran Emmett O'Loughlin
2019 - 2022 Co-Supervisor Equivariant Oka theory for Riemann surfaces Master of Philosophy Master Full Time Mr Alexander Joseph Fausto Lai De Oliveira
2019 - 2022 Co-Supervisor Algebraic Oka Theory for Curves Master of Philosophy Master Full Time Mr Ryan James Dye
2019 - 2024 Principal Supervisor Higher differential geometry and non-integral Kac-Moody extensions Master of Philosophy Master Full Time Mr James Anthony McCusker
2017 - 2019 Co-Supervisor Bundle Gerbes and the Weyl Map Master of Philosophy Master Full Time Miss Kimberly Elise Becker
2017 - 2019 Co-Supervisor Holomorphic Immersions of Restricted Growth from Smooth Affine Algebraic Curves into the Complex Plane Master of Philosophy Master Full Time Mr Daniel Cody John
2016 - 2018 Co-Supervisor Lifting Bundle Gerbes and Central Extensions of Gauge Groups Master of Philosophy Master Full Time Mr Parsa Kavkani
2014 - 2017 Co-Supervisor Topics in Equivariant Cohomology Master of Philosophy Master Full Time Luke Francis Keating Hughes

Connect With Me

External Profiles

Other Links