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.

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.

Publications

Preprints

  1. n-cluster tilting subcategories from gluing systems of representation-directed algebras, arxiv.

Published

  1. Gluing of n-cluster tilting subcategories for representation-directed algebras, accepted for publication in Algebras and Representation Theory, online version, arxiv.

  2. Wide subcategories of d-cluster tilting subcategories with M. Herschend and P. Jorgensen, Transactions of the American Mathematical Society, online version, arxiv.

  3. n-Cluster tilting subcategories of representation-directed algebras, Journal of Pure and Applied Algebra, online version, arxiv.

Invited talks

  1. February 2020, Higher dimensional AR-theory through Nakayama algebas, Algebra Seminar, Aristotle University of Thessaloniki.

Contributed talks

  1. October 2019, Representations of quivers and Gabriel’s theorem, PhD Math Fest 2019, KTH Royal Institute of TechnologyStockholm University.

  2. April 2019, Gluing of n-cluster tilting subcategories for representation-directed algebras, Isfahan School and Conference on Representations of Algebras, University of Isfahan.

  3. September 2018, Quiver Grassmanians, PhD Seminar, Uppsala University.

  4. August 2018, Gluing of n-cluster tilting subcategories for representation-directed algebras, International Conference on Representations of Algebras, Czech Technical University in Prague.

  5. December 2017, Dyck paths corresponding to 2-Gorenstein acyclic Nakayama algebras, PhD Seminar, Uppsala University.

  6. May 2017, An introduction to higher dimensional AuslanderReiten theory, Mini-Conference for PhD-Students in Mathematics, Stockholm University.

  7. November 2016, Colouring the AuslanderReiten quiver of a Nakayama algebra, PhD Seminar, Uppsala University.

  8. August 2016, n-cluster tilting subcategories of Nakayama algebras, International Conference on Representations of Algebras, Syracuse University.

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

  10. June 2015, n-cluster tilting modules over quotients of path algebras of type A, Algebra and Geometry Seminar, Uppsala University.

Teaching

Main lecturer

  1. Algebraic Structures (2019, 2018), Uppsala University.

  2. Linear Algebra II (2017), Uppsala University.

Thesis supervisor

  1. Bachelor thesis of Bim Gustavsson: Representations of Finite-Dimensional Algebras and Gabriel’s Theorem (2019), Uppsala University.

Teaching assistant

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

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

  3. 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