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. 

Groups

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
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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
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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