Hi! I'm Matti, I am a PhD student at Uppsala University. My supervisor is Volodymyr Mazorchuk, and my co-supervisor is Julian Külshammer.
My research interests include:
2-representations and module categories over 2-categories and monoidal categories, especially in representation theoretic settings
Tambara modules
Temperley-Lieb categories, categories of webs
non-rigid monoidal categories
Papers
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
Identity in the presence of adjunction. arXiv: 2401.09892
Module categories, internal bimodules and Tambara modules. arXiv: 2210.13443 (submitted)
Talks
"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)
Since 2021, I'm the president of Uppsala Mathematics Association, a small organization with a long (Est. 1853!) history of supporting and promoting mathematics in Uppsala. Nowadays we mainly promote 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. See more at the association's website (in English!).