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:
- Higher-dimensional Auslander–Reiten theory
- Homological dimensions
- \(\tau\)-tilting theory
- Geometric models in representation theory
Writings
Preprints
- Higher homological algebra for one-point extensions of bipartite hereditary algebras and spectral graph theory, with K. M. Jacobsen and M. H. Sandøy (2024).
- \(\tau_d\)-tilting theory for linear Nakayama algebras, with E. S. Rundsveen (2024).
- \(n\)-cluster tilting subcategories from gluing systems of representation-directed algebras (2020).
Publications
- \(n\mathbb{Z}\)-cluster tilting subcategories for Nakayama algebras, with M. Herschend and S. Kvamme, Mathematische Zeitschrift (2024).
- \(n\)-cluster tilting subcategories for radical square zero algebras, Journal of Pure and Applied Algebra (2022).
- Existence of a \(2\)-cluster tilting module does not imply finite complexity, with R. Marczinzik, Journal of Algebra (2022).
- Gluing of \(n\)-cluster tilting subcategories for representation-directed algebras, Algebras and Representation Theory (2020).
- Wide subcategories of \(d\)-cluster tilting subcategories, with M. Herschend and P. Jorgensen, Transactions of the American Mathematical Society (2020).
- \(n\)-Cluster tilting subcategories of representation-directed algebras, Journal of Pure and Applied Algebra. (2019).
PhD Thesis
- Constructions of n-cluster tilting subcategories using representation-directed algebras, Uppsala University (2020).
Code
- 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.
- 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
- 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
- August 2024: Higher \(\tau\)-tilting theory for Nakayama algebras at the International Conference on Representations of Algebras 2024, Shanghai Jiao Tong University. Slides
- April 2024: \(\tau_d\)-tilting theory for Nakayama algebras at the Spring Workshop on the Representation Theory of Algebras and related algebras, OIST. Slides
- March 2024: \(\tau_d\)-tilting theory for Nakayama algebras at the Algebra seminar, Uppsala University.
- November 2023: \(\tau_d\)-tilting theory for Nakayama algebras at the Homological Algebra Symposium, Aarhus University.
- 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.
- 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
- 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.
- January 2023: \(n\)-cluster tilting subcategories for truncated path algebras at the FD Seminar. Slides
- 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.
- August 2022: \(n\)-cluster tilting subcategories for truncated path algebras at the 28th Nordic Congress of Mathematicians (Representation theory session), Aalto University. Slides
- 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
- 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
- November 2021: Constructions of n-cluster tilting subcategories at the Algebra seminar, Norwegian University of Science and Technology.
- February 2021: \(n\)-cluster tilting modules for radical square zero algebras at The TRAC seminar, Université de Sherbrooke. Slides
- 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
- February 2020: Higher dimensional AR-theory through Nakayama algebras at the Algebra seminar, Aristotle University of Thessaloniki.
- October 2019: Representations of quivers and Gabriel's theorem at the PhD Math Fest 2019, KTH Royal Institute of Technology-Stockholm University.
- 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.
- September 2018: Quiver Grassmanians at the PhD Seminar, Uppsala University.
- 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.
- December 2017: Dyck paths corresponding to \(2\)-Gorenstein acyclic Nakayama algebras at the PhD Seminar, Uppsala University.
- May 2017: An introduction to higher dimensional Auslander–Reiten theory at the Mini-Conference for PhD-Students in Mathematics, Stockholm University.
- November 2016: Colouring the Auslander–Reiten quiver of a Nakayama algebra at the PhD Seminar, Uppsala University.
- August 2016: \(n\)-cluster tilting subcategories of Nakayama algebras at the International Conference on Representations of Algebras 2016, Syracuse University.
- June 2016: \(n\)-cluster tilting subcategories of Nakayama algebras at the Representation Theory Conference 2016, Uppsala University.
- June 2015: \(n\)-cluster tilting modules over quotients of path algebras of type \(A\) at the Algebra and Geometry Seminar, Uppsala University.
Travel
Future
- June 2025, Geometric Models in Representation Theory and Beyond , NTNU.
Past conferences and workshops
- December 2024, Representation theory - combinatorial aspects and applications to TDA, NTNU.
- August 2024, International Conference on Representations of Algebras 2024, Shanghai Jiao Tong University.
- April 2024, Spring Workshop on the Representation Theory of Algebras and related algebras, OIST.
- January 2024, Flash Talks in Representation Theory 2024, NTNU (online).
- July 2023, Homological Algebra and Representation Theory, University of the Aegean.
- July 2023, 29th Nordic Congress of Mathematicians, Aalborg university.
- March 2023, Combinatorial aspects of Representation Theory, Center for Advanced Studies Oslo.
- January 2023, Flash Talks in Representation Theory 2023, NTNU (online).
- August 2022, 28th Nordic Congress of Mathematicians, Aalto University.
- August 2022, International Conference on Representations of Algebras 2022, Universidad de la República and de Buenos Aires.
- July 2022, Second Congress of Greek Mathematicians, Hellenic Mathematical Society.
- June 2022, Triangulated categories in representation theory and beyond, The Abel symposium 2022.
- June 2022, Øyvind 60, Algebra group at NTNU.
- May 2022, Online Workshop on Higher Dimensional Homological Algebra, IPM-Isfahan and University of Isfahan (online).
- January 2022, Geometric and homological methods in representation theory, Lancaster University (online).
- January 2022, Flash Talks in Representation Theory 2022, NTNU (online).
- September 2021, Conference in celebration of the work of Bill Crawley-Boevey, Universität Bielefeld (online).
- June 2021, Braids, mutations and twists in algebra and geometry, Uppsala University (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 2021, NTNU (online).
- November 2020, International Conference on Representations of Algebras 2020, (online).
- October 2020, 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 and 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, Idun 75, NTNU.
- 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.
Past research visits
- 28.10.2024–31.10.2024, Centre for Advanced Study Oslo, under the project Geometric Methods in Higher Homological Algebra, Oslo, Norway.
- 08.10.2022–29.10.2022, Centre for Advanced Study Oslo, under the project Representation Theory: Combinatorial Aspects and Applications, Oslo, Norway.
- 26.02.2020–29.02.2020, visited Chrysostomos Psaroudakis at the Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, Greece.
Teaching
Main lecturer
- Rings and modules (2023), NTNU.
- Galois theory (2024, 2023), NTNU.
- Homological algebra (2022), NTNU (substitute of the main lecturer for the last third of the course).
- Algebraic Structures (2019, 2018), Uppsala University.
- Linear Algebra II (2017), Uppsala University.
Thesis supervision
- Bachelor thesis of Mathea Josefine Falkman Swensson: En kort introduksjon til Nakayama-algebraer (2024), NTNU.
- Bachelor thesis of Mia Soheltberg: Triangulated structure of stable Frobenius categories and derived abelian categories (2024), NTNU.
- Bachelor thesis of Bim Gustavsson: Representations of Finite-Dimensional Algebras and Gabriel’s Theorem (2019), Uppsala University.
Reading seminars
- Representation-theory of Cohen–Macaulay modules (2023), NTNU (together with Sondre Kvamme).
- Calabi–Yau structures for triangulated categories (2022), NTNU (together with Sondre Kvamme).
Teaching assistant
- Linear Algebra II (2019, 2018, 2016), Uppsala University.
- Probability and Statistics (2017, 2016), Uppsala University.
- Several Variable Calculus (2016), Uppsala University.
Event organisation
- June 2024, Geometric Models in Representation Theory and Beyond (member of the organising committee), NTNU.
- September 2023–August 2024, Algebra seminar of the NTNU algebra group, organised together with Mads H. Sandøy.
- March 2020, Uppsala Ph.D. Mathematics Conference (member of the organising committee), Uppsala University.
Outreach
- September 2024, Researchers' Night 2024, NTNU, topic: Explore whimsical games.
- September 2023, Researchers' Night 2023, NTNU, topic: What is the shape of a bubble?.
- September 2023, Hyfer festival, NTNU, topic: The art of mathematics.
- September 2022, Researchers' Night 2022, NTNU, topic: The world's most difficult equation.
Contact
Feel free to reach me at laertis.vaso@gmail.com.