Hey, I'm Roma (he/him) and this is my professional webpage. I do mathematics somewhere at the crossroads of metric geometry, geometric topology and discrete geometry, though I quite enjoy learning about all flavors of geometry and topology. I try to be open to anything interesting, so feel free to email me if you have suggestions!
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Though this is a professional webpage, I feel now a necessity to put my personal statement here. The current actions of the Russian government cannot be justified and understood. They are people without any shame or common sense. The war needs to be stopped, and as with many reasonable Russian people, I stand with Ukraine in this horrible historical moment.
Contacts: rprosanov@gmail.com
Positions:
since 2025: Autonomous University of Barcelona, Postdoc
2025: Technical University of Vienna, Postdoc
2022 - 2025: University of Vienna, Postdoc
2020 - 2021: Technical University of Vienna, Postdoc
Education:
2019 - 2020: Technical University of Vienna, PhD Student
2017 - 2019: University of Fribourg, PhD Student
Supervisor: Ivan Izmestiev, [Thesis]
2011 - 2017: Moscow State University, Diploma studies
Supervisor: Andrei Raigorodskii
Grants, Awards:
2025 - 2028: Schrödinger fellowship of FWF (the Austrian Science Fund) with the project Hyperbolic and pseudo-hyperbolic geometric structures, grant J4955
The award (Studienpreis) of the Austrian Mathematical Society (2022) for a doctoral thesis in mathematics
2022 - 2025: PI of the project Rigidity and flexibility of anti-de Sitter 3-manifolds, grant ESP-12-N of FWF (the Austrian Science Fund)
Preprints:
(with Jean-Marc Schlenker) Rigidity of anti-de Sitter (2+1)-spacetimes with convex boundary near the Fuchsian locus (2025), [arxiv]
Hyperbolic 3-manifolds with boundary of polyhedral type (2022), [arxiv]
Papers:
(with François Fillastre) Polyhedral surfaces in flat (2+1)-spacetimes and balanced cellulations on hyperbolic surfaces (2025)
Journal für die reine und angewandte Mathematik (Crelle's Journal), 822, 259-316 (2025), [journal], [arxiv]
Dual metrics on the boundary of strictly polyhedral hyperbolic 3-manifolds (2022)
To appear in Journal of Differential Geometry, [arxiv]
(with Ivan Izmestiev and Tianqi Wu) Prescribed curvature problem for discrete conformality on convex spherical cone-metrics
Advances in Mathematics, 437, 35 p. (2024), [journal], [arxiv]
(with Semyon Alesker and Mikhail Katz) New invariants of Gromov-Hausdorff limits of Riemannian surfaces with curvature bounded below
Geometriae Dedicata, 217:12, 1-44 (2023), [journal], [arxiv]
Rigidity of compact Fuchsian manifolds with convex boundary
International Mathematics Research Notices, 2023:3, 1959-2094 (2023), [journal], [arxiv]
On a relation between packing and covering densities of convex bodies
Discrete and Computational Geometry, 65, 1028–1037 (2021), [journal], [conference], [arxiv]
Ideal polyhedral surfaces in Fuchsian manifolds
Geometriae Dedicata, 206, 151–179 (2020), [journal], [arxiv]
Chromatic numbers of spheres
Discrete Mathematics, 341:11, 3123–3133 (2018), [journal], [arxiv]
Counterexamples to Borsuk’s conjecture with large girth
Mathematical Notes, 105:5–6, 874–880 (2019), [journal]
A new proof of the Larman–Rogers upper bound for the chromatic number of the Euclidean space
Discrete Applied Mathematics, 276, 115–120 (2020), [journal], [arxiv]
Upper bounds for the chromatic numbers of Euclidean spaces with forbidden Ramsey sets
Mathematical Notes, 103:1–2, 243–250 (2018), [journal]
(with Andrei Raigorodskii and Arsenii Sagdeev) Improvements of the Frankl–Rődl theorem and geometric consequences
Doklady Mathematics, 96:1, 336–338 (2017), [journal]
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