Martina Rovelli

MSI Fellow

Since July 2019 I am an MSI Fellow at the Australian National University, part of the Algebra&Topology group. I was also a postdoctoral member of the MSRI program on Higher categories and categorification during January-May 2020. Before ANU, I was a Postdoctoral Fellow of the Swiss NSF at Johns Hopkins, working with Emily Riehl. I got my PhD in 2017 at EPF Lausanne (Switzerland), under the supervision of Kathryn Hess.

Research interests

I do algebraic topology, homotopy theory and higher category theory. 

My current research, joint in different combinations with Julie BergnerDaniel Fuentes-KeuthanMagdalena Kedziorek, and Viktoriya Ozornova, focuses on studying the homotopy theory of higher categories (e.g., comparing models of (∞,n)-categories and developing certain aspects of the theory of (∞,1)-categories). 

I also have a series of papers (joint with Julie BergnerAngélica OsornoViktoriya Ozornova and Claudia Scheimbauer) on the topic of 2-Segal spaces and their relation with the Waldhausen construction. 

My PhD thesis focused on the study of homotopy invariants of principal bundles and geometric interpretations of characteristic classes. 


Higher categories

  • Gray tensor product and saturated N-complicial sets, with V.Ozornova and D.Verity, 2020: arXiv
  • Fundamental pushouts of n-complicial sets, with V.Ozornova, 2020: arXiv
  • The Duskin nerve of 2-categories in Joyal's cell category Θ_2, with V.Ozornova, 2019, J. Pure Appl. Algebra: arXivdoi
  • Weighted limits in an (∞,1)-category, 2019: arXiv
  • Nerves of 2-categories and categorification of (∞,2)-categories, with V.Ozornova, 2019: arXiv
  • A model structure on prederivators for (∞,1)-categories, with D.Fuentes-Keuthan and M.Kedziorek, 2018, Theory Appl. Categ.: arXivdoipdf
  • Model structures for (∞,n)-categories on (pre)stratified simplicial sets and prestratified simplicial spaces, with V.Ozornova, 2018, Algebr. Geom. Topol.: arXivdoi

2-Segal spaces

  • Comparison of Waldhausen constructions, with J.Bergner, A.Osorno, V.Ozornova and C.Scheimbauer, 2019, Ann. K-Theory: arXiv
  • 2-Segal objects and the Waldhausen construction, with J.Bergner, A.Osorno, V.Ozornova and C.Scheimbauer, 2018, Algebr. Geom. Topol.: arXivjournal
  • The edgewise subdivision criterion for 2-Segal objects, with J.Bergner, A.Osorno, V.Ozornova and C.Scheimbauer, 2018, Proc. Amer. Math. Soc.: arXivdoi
  • The unit of the total décalage adjunction, with V.Ozornova, 2017, J. Homotopy Relat. Struct.: arXivdoipdf
  • 2-Segal sets and the Waldhausen construction, with J.Bergner, A.Osorno, V.Ozornova and C.Scheimbauer, 2016, Topology Appl.: arXivdoi

Bundles and characteristic classes

  • Characteristic classes as complete obstructions, 2016, J. Homotopy Relat. Struct.: arXivdoipdf
  • A looping-delooping adjunction for topological spaces, 2015, Homology Homotopy Appl.: arXivdoipdf
  • Towards new invariants for principal bundles, 2017, PhD Thesis: EPFL doi