Since October 2020 I am a postdoctroal fellow at the Max-Planck-Institut für Mathematik in Bonn. My mentor is Jan Schröer. I completed my PhD at Uppsala University under the supervision of Martin Herschend. My research is in representation theory of finite-dimensional algebras, mainly concerning higher dimensional Auslander–Reiten theory and the global dimension of algebras.
A crucial notion in higher dimensional Auslander–Reiten theory is that of the so-called n-cluster tilting modules and subcategories. Furthermore, due to the homological nature of this theory, an important role is played by the global dimension of the underlying algebra. In my research I try to answer questions about both of these notions.
First I try to construct and classify n-cluster tilting modules and subcategories that exhibit interesting properties. Secondly, I am interested in the global dimension of algebras, especially those which admit n-cluster tilting modules. To these ends I have been focusing on some special classes of algebras like Nakayama algebras and representation-directed algebras and used tools such as algebra epimorphisms and categorical limits to construct algebras where one can both confirm the existence of an n-cluster tilting module and control the global dimension.
Existence of a 2-cluster tilting module does not imply finite complexity, with R. Marczinzik, arxiv.
n-cluster tilting subcategories from gluing systems of representation-directed algebras, arxiv.
April 2019, Gluing of n-cluster tilting subcategories for representation-directed algebras, Isfahan School and Conference on Representations of Algebras, University of Isfahan.
September 2018, Quiver Grassmanians, PhD Seminar, Uppsala University.
August 2018, Gluing of n-cluster tilting subcategories for representation-directed algebras, International Conference on Representations of Algebras, Czech Technical University in Prague.
December 2017, Dyck paths corresponding to 2-Gorenstein acyclic Nakayama algebras, PhD Seminar, Uppsala University.
November 2016, Colouring the Auslander–Reiten quiver of a Nakayama algebra, PhD Seminar, Uppsala University.
August 2016, n-cluster tilting subcategories of Nakayama algebras, International Conference on Representations of Algebras, Syracuse University.
November 2020, International Conference on Representations of Algebras 2020 (online),
Bachelor thesis of Bim Gustavsson: Representations of Finite-Dimensional Algebras and Gabriel’s Theorem (2019), Uppsala University.
email: vaso @ mpim-bonn dot mpg dot de
Max-Planck-Institut für Matematik