About Me

I am a mathematician specialising in Algebra. From October 2021 to September 2024, I was a postdoctoral fellow at the Department of Mathematical Sciences of the Norwegian University of Science and Technology, under the mentorship of Steffen Oppermann. Previously, I held a postdoctoral position at the Max Planck Institute for Mathematics in Bonn, mentored by Jan Schröer. Before that, I completed my PhD at the Department of Mathematics of Uppsala University, supervised by Martin Herschend.

Research Interests

My research primarily revolves around the representation theory of finite-dimensional algebras. Some topics I like to think about are:

I also like using computer programs during my work, both for computational and visualization purposes.

Writings

Preprints

  1. Higher homological algebra for one-point extensions of bipartite hereditary algebras and spectral graph theory, with K. M. Jacobsen and M. H. Sandøy (2024).
    Cite arXiv
  2. \(\tau_d\)-tilting theory for linear Nakayama algebras, with E. S. Rundsveen (2024).
    Cite arXiv Visualize Code
  3. \(n\)-cluster tilting subcategories from gluing systems of representation-directed algebras (2020).
    Cite arXiv

Publications

  1. \(n\mathbb{Z}\)-cluster tilting subcategories for Nakayama algebras, with M. Herschend and S. Kvamme, Mathematische Zeitschrift (2024).
    Cite Journal arXiv
  2. \(n\)-cluster tilting subcategories for radical square zero algebras, Journal of Pure and Applied Algebra (2022).
    Cite Journal arXiv
  3. Existence of a \(2\)-cluster tilting module does not imply finite complexity, with R. Marczinzik, Journal of Algebra (2022).
    Cite Journal arXiv
  4. Gluing of \(n\)-cluster tilting subcategories for representation-directed algebras, Algebras and Representation Theory (2020).
    Cite Journal arXiv
  5. Wide subcategories of \(d\)-cluster tilting subcategories, with M. Herschend and P. Jorgensen, Transactions of the American Mathematical Society (2020).
    Cite Journal arXiv
  6. \(n\)-Cluster tilting subcategories of representation-directed algebras, Journal of Pure and Applied Algebra. (2019).
    Cite Journal arXiv

PhD Thesis

  1. Constructions of n-cluster tilting subcategories using representation-directed algebras, Uppsala University (2020).

Code

  1. https://github.com/laertisv/Higher_Tau_Nakayama. HTML/CSS/JavaScript code for an interactive website to compute and visualize \(\tau_d\)-rigid pairs, mutations of strongly maximal \(\tau_d\)-rigid pairs and \(d\)-torsion classes for linearly oriented Nakayama algebras with homogeneous relations which admit a \(d\)-cluster tilting subcategory. Created together with Endre S. Rundsveen.
  2. https://github.com/laertisv/d_torsion_classes. A Python script for computations in higher \(\tau\)-tilting theory for linear Nakayama algebras with homogeneous relations which admit a \(d\)-cluster tilting subcategory. Among other things, the script computes all \(d\)-torsion classes and the corresponding summand maximal \(\tau_d\)-rigid pairs.

Talks

Future

Past

  1. December 2024: Higher \(\tau\)-tilting theory for linear Nakayama algebras at the conference Representation Theory – Combinatorial Aspects and Applications to TDA, Norwegian University of Science and Technology. Slides
  2. August 2024: Higher \(\tau\)-tilting theory for Nakayama algebras at the International Conference on Representations of Algebras 2024, Shanghai Jiao Tong University. Slides
  3. April 2024: \(\tau_d\)-tilting theory for Nakayama algebras at the Spring Workshop on the Representation Theory of Algebras and related algebras, OIST. Slides
  4. March 2024: \(\tau_d\)-tilting theory for Nakayama algebras at the Algebra seminar, Uppsala University.
  5. November 2023: \(\tau_d\)-tilting theory for Nakayama algebras at the Homological Algebra Symposium, Aarhus University.
  6. July 2023: \(2\)-hereditary quadratic monomial algebras via one-point extensions of bipartite graphs at the conference Homological Algebra and Representation Theory, University of the Aegean.
  7. July 2023: \(2\)-representation-finite quadratic monomial algebras via one-point extensions of bipartite graphs at the 29th Nordic Congress of Mathematicians (Representation Theory and Combinatorics session), Aalborg University. Slides
  8. March 2023: \(2\)-hereditary quadratic monomial algebras via one-point extensions of bipartite graphs at the conference Combinatorial Aspects of Representation Theory, Center for Advanced Studies, Oslo.
  9. January 2023: \(n\)-cluster tilting subcategories for truncated path algebras at the FD Seminar. Slides
  10. October 2022: Quadratic monomial \(2\)-hereditary algebras and generalizations during research visit linked to the project Representation Theory: Combinatorial Aspects and Applications, Center for Advanced Studies, Oslo.
  11. August 2022: \(n\)-cluster tilting subcategories for truncated path algebras at the 28th Nordic Congress of Mathematicians (Representation theory session), Aalto University. Slides
  12. August 2022: \(n\)-cluster tilting subcategories for truncated path algebras at the International Conference on Representations of Algebras 2022, Universidad de la República-Universidad de Buenos Aires. Slides
  13. July 2022: Truncated path algebras in higher-dimensional Auslander–Reiten theory at the Second Congress of Greek Mathematicians (Algebra, Number Theory and Combinatorics session), National Technical University of Athens. Slides
  14. November 2021: Constructions of n-cluster tilting subcategories at the Algebra seminar, Norwegian University of Science and Technology.
  15. February 2021: \(n\)-cluster tilting modules for radical square zero algebras at The TRAC seminar, Université de Sherbrooke. Slides
  16. January 2021: \(n\)-cluster tilting modules for radical square zero algebras at the conference Flash Talks in Representation Theory at NTNU, Norwegian University of Science and Technology. Slides
  17. February 2020: Higher dimensional AR-theory through Nakayama algebras at the Algebra seminar, Aristotle University of Thessaloniki.
  18. October 2019: Representations of quivers and Gabriel's theorem at the PhD Math Fest 2019, KTH Royal Institute of Technology-Stockholm University.
  19. April 2019: Gluing of \(n\)-cluster tilting subcategories for representation-directed algebras at the Isfahan School and Conference on Representations of Algebras, University of Isfahan.
  20. September 2018: Quiver Grassmanians at the PhD Seminar, Uppsala University.
  21. August 2018: Gluing of \(n\)-cluster tilting subcategories for representation-directed algebras at the International Conference on Representations of Algebras 2018, Czech Technical University in Prague.
  22. December 2017: Dyck paths corresponding to \(2\)-Gorenstein acyclic Nakayama algebras at the PhD Seminar, Uppsala University.
  23. May 2017: An introduction to higher dimensional Auslander–Reiten theory at the Mini-Conference for PhD-Students in Mathematics, Stockholm University.
  24. November 2016: Colouring the Auslander–Reiten quiver of a Nakayama algebra at the PhD Seminar, Uppsala University.
  25. August 2016: \(n\)-cluster tilting subcategories of Nakayama algebras at the International Conference on Representations of Algebras 2016, Syracuse University.
  26. June 2016: \(n\)-cluster tilting subcategories of Nakayama algebras at the Representation Theory Conference 2016, Uppsala University.
  27. June 2015: \(n\)-cluster tilting modules over quotients of path algebras of type \(A\) at the Algebra and Geometry Seminar, Uppsala University.

Travel

Future

  1. June 2025, Geometric Models in Representation Theory and Beyond , NTNU.

Past conferences and workshops

  1. December 2024, Representation theory - combinatorial aspects and applications to TDA, NTNU.
  2. August 2024, International Conference on Representations of Algebras 2024, Shanghai Jiao Tong University.
  3. April 2024, Spring Workshop on the Representation Theory of Algebras and related algebras, OIST.
  4. January 2024, Flash Talks in Representation Theory 2024, NTNU (online).
  5. July 2023, Homological Algebra and Representation Theory, University of the Aegean.
  6. July 2023, 29th Nordic Congress of Mathematicians, Aalborg university.
  7. March 2023, Combinatorial aspects of Representation Theory, Center for Advanced Studies Oslo.
  8. January 2023, Flash Talks in Representation Theory 2023, NTNU (online).
  9. August 2022, 28th Nordic Congress of Mathematicians, Aalto University.
  10. August 2022, International Conference on Representations of Algebras 2022, Universidad de la República and de Buenos Aires.
  11. July 2022, Second Congress of Greek Mathematicians, Hellenic Mathematical Society.
  12. June 2022, Triangulated categories in representation theory and beyond, The Abel symposium 2022.
  13. June 2022, Øyvind 60, Algebra group at NTNU.
  14. May 2022, Online Workshop on Higher Dimensional Homological Algebra, IPM-Isfahan and University of Isfahan (online).
  15. January 2022, Geometric and homological methods in representation theory, Lancaster University (online).
  16. January 2022, Flash Talks in Representation Theory 2022, NTNU (online).
  17. September 2021, Conference in celebration of the work of Bill Crawley-Boevey, Universität Bielefeld (online).
  18. June 2021, Braids, mutations and twists in algebra and geometry, Uppsala University (online).
  19. May 2021, Virtual Advances in Representation Theory of Algebras 2021 (online).
  20. March 2021, Additive categories between algebra and functional analysis, (online).
  21. January 2021, Flash Talks in Representation Theory 2021, NTNU (online).
  22. November 2020, International Conference on Representations of Algebras 2020, (online).
  23. October 2020, Connections between representation theory and geometry, Hausdorff Research Institute for Mathematics (online).
  24. September 2020, 2020 Categorifications in Representation Theory, University of Leicester (online).
  25. October 2019, PhD Math Fest 2019, KTH Royal Institute of Technology and Stockholm University.
  26. April 2019, Isfahan School and Conference on Representations of Algebras, University of Isfahan.
  27. August 2018, International Conference on Representations of Algebras 2018, Czech Technical University in Prague.
  28. May 2017, Idun 75, NTNU.
  29. May 2017, Mini-Conference for PhD-Students in Mathematics, Stockholm University.
  30. September 2016, Algebraic mini-Workshop 2016, Uppsala University.
  31. August 2016, International Conference on Representations of Algebras 2016 , Syracuse University.
  32. June 2016, Representation Theory Conference 2016, Uppsala University.

Past research visits

  1. 28.10.2024–31.10.2024, Centre for Advanced Study Oslo, under the project Geometric Methods in Higher Homological Algebra, Oslo, Norway.
  2. 08.10.2022–⁠29.10.2022, Centre for Advanced Study Oslo, under the project Representation Theory: Combinatorial Aspects and Applications, Oslo, Norway.
  3. 26.02.2020–29.02.2020, visited Chrysostomos Psaroudakis at the Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, Greece.

Teaching

Main lecturer

  1. Rings and modules (2023), NTNU.
  2. Galois theory (2024, 2023), NTNU.
  3. Homological algebra (2022), NTNU (substitute of the main lecturer for the last third of the course).
  4. Algebraic Structures (2019, 2018), Uppsala University.
  5. Linear Algebra II (2017), Uppsala University.

Thesis supervision

  1. Bachelor thesis of Mathea Josefine Falkman Swensson: En kort introduksjon til Nakayama-algebraer (2024), NTNU.
  2. Bachelor thesis of Mia Soheltberg: Triangulated structure of stable Frobenius categories and derived abelian categories (2024), NTNU.
  3. Bachelor thesis of Bim Gustavsson: Representations of Finite-Dimensional Algebras and Gabriel’s Theorem (2019), Uppsala University.

Reading seminars

  1. Representation-theory of Cohen–Macaulay modules (2023), NTNU (together with Sondre Kvamme).
  2. Calabi–Yau structures for triangulated categories (2022), NTNU (together with Sondre Kvamme).

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.

Event organisation

  1. June 2024, Geometric Models in Representation Theory and Beyond (member of the organising committee), NTNU.
  2. September 2023–August 2024, Algebra seminar of the NTNU algebra group, organised together with Mads H. Sandøy.
  3. March 2020, Uppsala Ph.D. Mathematics Conference (member of the organising committee), Uppsala University.

Outreach

  1. September 2024, Researchers' Night 2024, NTNU, topic: Explore whimsical games.
  2. September 2023, Researchers' Night 2023, NTNU, topic: What is the shape of a bubble?.
  3. September 2023, Hyfer festival, NTNU, topic: The art of mathematics.
  4. September 2022, Researchers' Night 2022, NTNU, topic: The world's most difficult equation.

Contact

Feel free to reach me at laertis.vaso@gmail.com.