Viktoriya Ozornova

I am an advanced researcher at Max Planck Institute for Mathematics, Bonn. My research area is algebraic topology, focussing in particular on abstract homotopy theory.

Contact:

My e-mail address is firstname.lastname at mpim-bonn.mpg.de.
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News I have a master student working jointly with me and Paige North, based at the University of Utrecht.
Publications and Preprints 
  1. A model for the coherent walking ?-equivalence, [arXiv:2404.14509], [doi], joint with  Amar Hadzihasanovic,  F?lix Loubaton, and  Martina Rovelli, submitted,
  2. What is an equivalence in a higher category? [arXiv:2303.00567], joint with  Martina Rovelli, survey, to appear in Bulletin of London Mathematical Society;
  3. A Quillen adjunction between globular and complicial approaches to (∞,n)-categories, [arXiv:2206.02689], [doi], joint with  Martina Rovelli, appeared in Advances in Mathematics,  421 (2023), 108980
  4. Model independence of (∞,2)-categorical nerves, [arXiv:2206.00660], joint with Lyne Moser and  Martina Rovelli, submitted 
  5. Pushouts of Dwyer maps are (∞,1)-categorical, [arXiv:2205.02353], joint with  Philip Hackney,  Emily Riehl and  Martina Rovelli, to appear in Algebraic & Geometric Topology,  
  6. A categorical characterization of strong Steiner ω-categories, [arXiv:2204.12962], [doi] joint with  Dimitri Ara, Andrea Gagna, and  Martina Rovelli, appeared in Journal of Pure and Applied Algebra, 227 (2023), no. 7, 107313.
  7. An (∞, 2)-categorical pasting theorem, [arXiv:2106.03660], joint with  Philip Hackney,  Emily Riehl and  Martina Rovelli, appeared in Transactions of the American Mathematical Society, DOI: 8783 , 227 (2023), no. 1, 555-597,
  8. An explicit comparison between 2-complicial sets and Θ_2-spaces, [arXiv:2104.13292], joint with  Julie Bergner and  Martina Rovelli, to appear in Algebraic & Geometric Topology,  
  9. Nerves and cones of free loop-free ω-categories, [arXiv:2103.01066], joint with  Andrea Gagna, and  Martina Rovelli, appeared in Tunisian Journal of Mathematics  5 (2023), no. 2,  
  10. Gray tensor product and saturated N-complicial sets, [arXiv:2007.01235], joint with  Martina Rovelli and Dominic Verity, appeared in Higher Structures,  7 (2023), no. 1, 1-21,
  11. Fundamental pushouts of n-complicial sets,[arXiv:2005.05844], joint with  Martina Rovelli, appeared in Higher Structures,  6 (2022), no. 1,
  12. Stable homotopy hypothesis in the Tamsamani model,[arXiv:2001.05577], joint with Lyne Moser, Simona Paoli, Maru Sarazola, Paula Verdugo, appeared in Proceedings in Women in Topology III, Topology and its Applications, no. 316, 2022
  13. The Duskin nerve of 2-categories in Joyal's cell category Θ_2, [arXiv:1910.06103], [doi], joint with  Martina Rovelli, appeared in Journal of Pure and Applied Algebra, 225 (2021), no. 1, 106462.
  14. Nerves of 2-categories and 2-categorification of  (∞, 2)-categories, [arXiv:1902.05524], [doi], joint with  Martina Rovelli, appeared in Advances in Mathematics,  391 (2021), 107948
  15. Comparison of Waldhausen constructions, [arXiv:1901.03606], [doi], joint with  Julie Bergner, Angélica M. Osorno, Martina Rovelli, Claudia Scheimbauer, appeared in Annals of K-Theory,  6  (2021), no. 1, 97-136
  16. Rings of modular forms and a splitting of TMF0(7), [arXiv:1812.04425], [doi] joint with   Lennart Meier, with a joint appendix with Martin Olbermann, appeared in Selecta Mathematica,  26 (2020), no. 1, Paper No. 7, 73 pp.
  17. 2-Segal objects and the Waldhausen construction, [arXiv:1809.10924], [doi], joint with  Julie Bergner, Angélica M. Osorno, Martina Rovelli, Claudia Scheimbauer,  appeared in Algebraic & Geometric Topology, 21  (2021), no. 3, 1267-1326
  18. Model structures for (∞, n)-categories on (pre)stratified simplicial sets and prestratified simplicial spaces, [arXiv:1809.10621], [doi], joint with  Martina Rovelli,  appeared in Algebraic & Geometric Topology, 20  (2020), no. 3, 1543--1600.
  19. The edgewise subdivision criterion for 2-Segal objects,[arXiv:1807.05069], [doi], joint with   Julie Bergner, Angélica M. Osorno, Martina Rovelli, Claudia Scheimbauer, appeared in Proceedings of the AMS, 148 (2020), no. 1, 71--82.
  20. The unit of the total décalage adjunction [arXiv:1711.03451], [doi], joint with Martina Rovelli, appeared in Journal of Homotopy and Related Structures, 15 (2020), no. 2, 333--349.
  21. 2-Segal sets and the Waldhausen construction [arXiv:1609.02853], [doi], joint with  Julie Bergner, Angélica M. Osorno, Martina Rovelli, Claudia Scheimbauer,   appeared in Proceedings of WIT II, Topology and its Applications, no. 235, pp. 445-484, 2018
  22. Discrete Morse Theory and a Reformulation of the K(π,1)-conjecture, [arXiv:1309.1337], [doi],  appeared in Communications in Algebra 45 (2017), no. 4, 1760-1784.
  23. A model structure on GCat [arXiv:1311.4605], [doi], joint with Anna Marie Bohmann, Kristen Mazur, Angélica M. Osorno, Kate Ponto, Carolyn Yarnall, appeared in Women in Topology: Collaborations in Homotopy Theory, Contemporary Mathematics, 2015
  24. Fibrancy of Partial Model Categories, joint with Lennart Meier [arXiv:1408.2743], [doi],  appeared in Homology, Homotopy and Applications, Volume 17.2 (2015), 53-80.
  25. Factorability, String Rewriting and Discrete Morse Theory, joint with Alexander Heß [arXiv:1412.3025], submitted
Supervision 

PhD Thesis

Master Theses

Bachelor Theses

 
Conferences organized
Other Writing

Moduli stack of elliptic curves, Version 0.3, joint with Lennart Meier - here, we collected the argument - well-known to the experts - for the stack property of the moduli stack of elliptic curves.  

Previous Teaching