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, representation-directed algebras and radical square zero algebras and I have 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.
n-cluster tilting subcategories for radical square zero algebras, arxiv.
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.
September 2021, Conference in celebration of the work of Bill Crawley-Boevey (online).
June 2021, Braids, mutations and twists in algebra and geometry (online).
May 2021, Virtual Advances in Representation Theory of Algebras 2021 (online).
March 2021, Additive categories between algebra and functional analysis (online).
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