## Short CV

Since January 2021, I am an Assistant Professor at

University of Massachusetts Amherst.
Before, I was an MSI Fellow at the

Australian National University (2019-2021),
a postdoctoral member of the

MSRI program
on

Higher categories and categorification (Spring 2020),
and a Postdoctoral Fellow of the Swiss NSF at

Johns Hopkins (2017-2019).
I got my PhD in 2017 at

EPF Lausanne Switzerland, under the supervision of

Kathryn Hess.
My research is supported by the

NSF grant 2203915.

## Research Interests

Higher category theory
Homotopy theory
Algebraic topology
These papers develop certain aspects of the theory of ω-categories.

** A model for the coherent walking ω-equivalence**, with A.Hadzihasanovic, F.Loubaton, V.Ozornova, 2024:
arXiv,
** What is an equivalence in a higher category?**, with V.Ozornova, 2023,
*Bull. London Math.*:
arXiv,
doi
** A categorical characterization of strong Steiner ω-categories**, with D.Ara, A.Gagna and V.Ozornova, 2022,
*J. Pure Appl. Algebra*:
arXiv,
doi
** Nerves and cones of free loop-free ω-categories**, with A.Gagna and V.Ozornova, 2021, *Tunis. J. Math.*:
arXiv,
pdf
These papers develop certain aspects of the theory of (∞,n)-categories or new model categories for (∞,n)-categories for general n.

** (∞,n)-Limits II: Comparison across models**, with L.Moser and N.Rasekh, 2024:
arXiv
** (∞,n)-Limits I: Definition and first consistency results**, with L.Moser and N.Rasekh, 2023:
arXiv
** An (∞,n)-categorical straightening-unstraightening construction**, with L.Moser and N.Rasekh, 2023:
arXiv
** A homotopy coherent nerve for (∞,n)-categories**, with L.Moser and N.Rasekh, 2022, *J. Pure Appl. Algebra*:
arXiv,
doi,
pdf
** A Quillen adjunction between globular and complicial approaches to (∞,n)-categories**, with V.Ozornova, 2022,
*Adv. Math*:
arXiv,
doi
** Gray tensor product and saturated N-complicial sets**, with V.Ozornova and D.Verity, 2020: *High. Struct.*:
arXiv,
doi,
pdf
** Fundamental pushouts of n-complicial sets**, with V.Ozornova, 2020,
*High. Struct.*:
arXiv,
doi,
pdf
** Model structures for (∞,n)-categories on (pre)stratified simplicial sets and spaces**, with V.Ozornova, 2018,
*Algebr. Geom. Topol.*:
arXiv,
doi
These papers
develop certain aspects of the theory of (∞,2)-categories or new model categories for (∞,2)-categories. Most of my work focuses on the model of 2-complicial sets.

** Model independence of (∞,2)-categorical nerves**, with L.Moser and V.Ozornova, 2022:
arXiv
** An (∞,2)-categorical pasting theorem**, with P.Hackney, V.Ozornova and E.Riehl, 2021,
*Trans. Am. Math. Soc.*:
arXiv,
doi
** An explicit comparison between Θ_2-spaces and 2-complicial sets**, with J.Bergner and V.Ozornova, 2021:
*Algebr. Geom. Topol.*:
arXiv
** The Duskin nerve of 2-categories in Joyal's cell category Θ_2**, with V.Ozornova, 2019,
*J. Pure Appl. Algebra*:
arXiv,
doi
** Nerves of 2-categories and categorification of (∞,2)-categories**, with V.Ozornova, 2019,
*Adv. Math*:
arXiv,
doi
These papers develop certain aspects of the theory of (∞,1)-categories or new model categories for (∞,1)-categories.

** Pushouts of Dwyer maps are (∞,1)-categorical**, with P.Hackney, V.Ozornova and E.Riehl, 2022
*Algebr. Geom. Topol.*:
arXiv, doi
** Induced model structures for ∞-categories and ∞-groupoids**, with P.Hackney, 2021,
*Proc. Amer. Math. Soc.*:
arXiv,
doi
** Weighted limits in an (∞,1)-category**, 2019,
*Appl. Categorical Struct.*:
arXiv,
doi,
pdf
** A model structure on prederivators for (∞,1)-categories**, with D.Fuentes-Keuthan and M.Kedziorek, 2018,
*Theory Appl. Categ.*:
arXiv,
doi,
pdf
This series of papers is on the topic of 2-Segal spaces and their relation with the Waldhausen construction.

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

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

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