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
