**Laertis Vaso**

### 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.

## Research interests

### 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.

*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 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.

## Publications

### Preprints

*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.

### Published

*Gluing of n-cluster tilting subcategories for representation-directed algebras*, Algebras and Representation Theory, online version, arxiv.*Wide subcategories of d-cluster tilting subcategories*with M. Herschend and P. Jorgensen, Transactions of the American Mathematical Society, online version, arxiv.*n-Cluster tilting subcategories of representation-directed algebras*, Journal of Pure and Applied Algebra, online version, arxiv.

## Invited talks

February 2021,

*n-cluster tilting modules for radical square zero algebras*, The TRAC seminar, Université de Sherbrooke, slides.January 2021,

*n-cluster tilting modules for radical square zero algebras*, Flash Talks in Representation Theory at NTNU, Norwegian University of Science and Technology, slides.February 2020,

*Higher dimensional AR-theory through Nakayama algebas*, Algebra Seminar, Aristotle University of Thessaloniki.

## Contributed talks

October 2019,

*Representations of quivers and Gabriel’s theorem,**PhD Math Fest 2019*, KTH Royal Institute of Technology–Stockholm University.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.May 2017,

*An introduction to higher dimensional Auslander*–*Reiten theory*, Mini-Conference for PhD-Students in Mathematics, Stockholm 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.June 2016,

*n-cluster tilting subcategories of Nakayama algebras*, Representation Theory Conference 2016, Uppsala University.June 2015,

*n-cluster tilting modules over quotients of path algebras of type A*, Algebra and Geometry Seminar, Uppsala University.

## Conferences attended

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).

January 2021, Flash Talks in Representation Theory, NTNU (online).

November 2020, International Conference on Representations of Algebras 2020 (online).

October 2020, Winter School "Connections between representation theory and geometry", Hausdorff Research Institute for Mathematics (online).

September 2020, 2020 Categorifications in Representation Theory, University of Leicester (online).

October 2019,

*PhD Math Fest 2019*, KTH Royal Institute of Technology–Stockholm University.April 2019, Isfahan School and Conference on Representations of Algebras, University of Isfahan.

August 2018, International Conference on Representations of Algebras 2018, Czech Technical University in Prague.

May 2017, Mini-Conference for PhD-Students in Mathematics, Stockholm University.

September 2016, Algebraic mini-Workshop 2016, Uppsala University.

August 2016, International Conference on Representations of Algebras 2016 , Syracuse University.

June 2016, Representation Theory Conference 2016, Uppsala University.

## Teaching

### Main lecturer

Algebraic Structures (2019, 2018), Uppsala University.

Linear Algebra II (2017), Uppsala University.

### Thesis supervisor

Bachelor thesis of Bim Gustavsson:

*Representations of Finite-Dimensional Algebras and Gabriel’s Theorem*(2019), Uppsala University.

### Teaching assistant

Linear Algebra II (2019, 2018, 2016), Uppsala University.

Probability and Statistics (2017, 2016), Uppsala University.

Several Variable Calculus (2016), Uppsala University.

## Contact

email: vaso @ mpim-bonn dot mpg dot de

Max-Planck-Institut für Matematik

Vivatsgasse 7

53111 Bonn

Deutschland