Mateusz (Matti) Stroiński

Hi! I'm Matti. I'm a postdoctoral researcher at the University of Hamburg, working with the research group of Prof. Christoph Schweigert.

In Autumn 2025, my postdoctoral stay is funded by the Lundström-Åmans stipendiestiftelse, and from 2026, it will be funded by the Knut and Alice Wallenberg Foundation.

I received my PhD in 2025 from Uppsala University. My supervisor was Prof. Volodymyr Mazorchuk, and my co-supervisor was Prof. Julian Külshammer.

My primary research interest is the study of module categories over monoidal categories, in particular over tensor categories or as (finitary) 2-representations. I am very interested the applications of such structures in representation theory, Hopf theory and in field theories. I'm also interested in such applications of other categorical structures, such as duoidal categories, multicategories or double categories.

CV & Contact

My current CV can be found here.

My email address is: matti at math dot uu dot se

Papers

A coboundary Temperley-Lieb category for sl2-crystals. Joint with Moaaz Alqady. Accepted for publication in Journal of the London Mathematical Society (2025).
Identity in the presence of adjunction. International Mathematics Research Notices (2024).
Module categories, internal bimodules, and Tambara modules. Proceedings of the London Mathematical Society 128(5)
Finite quotients of singular Artin monoids and categorification of the desingularization map. Joint with Helena Jonsson, Volodymyr Mazorchuk, Elin Persson Westin, Shraddha Srivastava and Xiaoyu Zhu. Journal of the Korean Mathematical Society 60(6): 1255-1302 (2023)
Weighted Colimits of 2-Representations and Star Algebras. Applied Categorical Structures 31(4) (2023)
Simple transitive 2-representations of bimodules over radical square zero Nakayama algebras via localization. Joint with Helena Jonsson. J. Algebra 613 (2023), 87–114
Simple transitive 2-representations of 2-categories associated to self-injective cores. Communications in Algebra, 50:8, 3630-3649 (2022)

Preprints

Hochschild cohomology for finitary 2-representations. Joint with James Macpherson and Vanessa Miemietz. arxiv:2503.09383
Simple algebras and exact module categories. Joint with Kevin Coulembier and Tony Zorman. arxiv:2501.06629
Reconstruction of module categories in the infinite and non-rigid settings. Joint with Tony Zorman. arxiv:2409.00793

Talks

"Characterisation of Module Categories in Terms of Algebras". BIREP Summer School on Finite Tensor Categories, Willebadessen, Germany. August 2025.
"A coboundary Temperley-Lieb category for sl2-crystals". Uppsala University, Uppsala Algebra Seminar. May 2025.
"Simple algebras and exact module categories". Université libre de Bruxelles, Hopf25. April 2025.
"Jacobson radicals and tensor categories". Uppsala University, Uppsala Algebra Seminar. February 2025.
“Tambara reconstruction and Morita theory for module categories over non-rigid monoidal categories”. Ohio State University, Quantum Symmetry Seminar. December 2024.
“Reconstruction for module categories over non-rigid monoidal categories”. University of Bonn, Oberseminar Representation Theory. November 2024.
“Module categories via (co)monads and (bi)algebraic structures”. Uppsala University, Uppsala Algebra Seminar. October 2024.
“Lax module profunctors, reconstruction, and tensor categories”. Univeristy of Ferrara, Hopf Algebras and Monoidal Categories. September 2024.
"Lax module functors, bialgebras and tensor categories''. Technische Universität Dresden, Seminar Geometric Methods in Mathematics. July 2024.
"Tambara reconstruction and tensor categories". INI satellite programme based at Gaelic College, Sabhal Mòr Ostaig, Topology, representation theory and higher structures. June 2024
"Tambara reconstruction". University of Georgia, Representation Theory and Related Geometry: Progress and Prospects. May 2024.
"Dual Objects And Adjoined Units In Semigroup Categories". San Francisco State University, AMS 2024 Spring Western Sectional Meeting. May 2024.
"Tambara reconstruction". Université catholique de Louvain, Seminar on Quantum groups, Hopf algebras and monoidal categories. April 2024.
"Identity in the presence of adjunction". Uppsala University, Uppsala Algebra Seminar. October 2023.
"Graphical calculus, linear algebra and categorical nonsense ". Uppsala University, PhD seminar. September 2023.
"Module categories via Tambara modules: reconstruction and enrichment". Technische Universität Dresden, Seminar Geometric Methods in Mathematics. July 2023.
"Categorical representation theory”. University of Oregon. A series of 8 talks on 2-representations of finitary 2-categories. April-June 2023.
“Jacobian conjecture and Weyl algebras”. University of Oregon, Graduate Student Algebra Seminar. April 2023.
“Categories as algebras: Morita theorems via profunctors”. University of Oregon, Graduate Student Algebra Seminar. January 2023.
“Pointless topology for sober spaces”. Uppsala University, PhD seminar. September 2022.
“Module categories and internal Morita equivalence”. Aalto University, 28th Nordic Congress of Mathematicians. August 2022.
“Weyl algebras and the Jacobian conjecture”. Uppsala University, PhD course in algebra. April 2022.
“Universal constructions in higher representation theory”. Svenska Matematikersamfundets höstmöte (Fall summit of Swedish Mathematical Society). November 2021.
“Weighted colimits of 2-representations”. University of East Anglia, UEA Pure Maths Seminar. November 2021.
“2-dimensional TQFTs and Frobenius algebras”. Uppsala University, PhD seminar. October 2021.
“Weighted colimits of 2-representations and star algebras”. Uppsala University, Uppsala Algebra Seminar. September 2021.
“Simple transitive 2-representations of bimodules via localization”. Uppsala University, Uppsala Algebra Seminar. December 2020.
“Self injective cores and (non-)cell 2-representations”. Uppsala University, Uppsala Algebra Seminar. April 2020

Matematiska föreningen i Uppsala (Uppsala Mathematics Association)

Between 2021 and 2025, I was the president of Uppsala Mathematics Association, a small organization with a long (Est. 1853!) history of supporting and promoting mathematics in Uppsala. Nowadays it mainly promotes mathematics among engineering and natural sciences students, by occasionally organizing talks, seminars and events, and by organizing the Association Summits (2 per year), where students receive Outstanding Student Awards. Recently (March 2025), we helped organize a movie screening! See more at the association's website (in English!).