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. 

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, arXiv.

2. τ_d-tilting theory for linear Nakayama algebras, with E. S. Rundsveen, arXiv.

3. n-cluster tilting subcategories from gluing systems of representation-directed algebras, arXiv.

Accepted for publication

1. nℤ-cluster tilting subcategories for Nakayama algebras, with M. Herschend and S. Kvamme, accepted in the Mathematische Zeitschrift, arXiv.

Published

1. n-cluster tilting subcategories for radical square zero algebras, Journal of Pure and Applied Algebra, online version, arXiv.

2. Existence of a 2-cluster tilting module does not imply finite complexity, with R. Marczinzik, Journal of Algebra, online version, arXiv.

3. Gluing of n-cluster tilting subcategories for representation-directed algebras,  Algebras and Representation Theory, online version, arXiv.

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

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

Future

Past

1. December 2024, Higher τ-tilting theory for linear Nakayama algebras, Representation theory - combinatorial aspects and applications to TDA, Norwegian University of Science and Technology, slides.

2. November 2023, τ_d-tilting theory for Nakayama algebras, Homological Algebra Symposium, Aarhus University.

3. July 2023, 2-hereditary quadratic monomial algebras via one-point extensions of bipartite graphs, Homological Algebra and Representation Theory, University of the Aegean.

4. July 2023, 2-representation-finite quadratic monomial algebras via one point extensions of bipartite graphs, 29th Nordic Congress of Mathematicians (Representation Theory and Combinatorics session), Aalborg university, slides.

5. March 2023, 2-hereditary quadratic monomial algebras via one point extensions of bipartite graphs, Combinatorial aspects of Representation Theory, Center for Advanced Studies Oslo.

6. January 2023, n-cluster tilting subcategories for truncated path algebras, FD seminar, slides.

7. October 2022, Quadratic monomial 2-hereditary algebras and generalizations, Representation Theory: Combinatorial Aspects and Applications, Center for Advanced Studies Oslo.

8. August 2022, n-cluster tilting subcategories for truncated path algebras, 28th Nordic Congress of Mathematicians (Representation theory session), Aalto University, slides.

9. July 2022, Truncated path algebras in higher-dimensional Auslander–Reiten theory, Second Congress of Greek Mathematicians (Algebra, Number Theory and Combinatorics session), National Technical University of Athens, slides.

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

11. 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.

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

1. April 2024, Higher τ-tilting theory for Nakayama algebras, International Conference on Representations of Algebras 2024, Shanghai Jiao Tong University, slides.

2. April 2024, τ_d-tilting theory for Nakayama algebras, Spring Workshop on the Representation Theory of Algebras and related algebras, OIST, slides.

3. March 2024, τ_d-tilting theory for Nakayama algebras, Algebra seminar, Uppsala University.

4. August 2022, n-cluster tilting subcategories for truncated path algebras, International Conference on Representations of Algebras 2022, Universidad de la República–Universidad de Buenos Aires, slides.

5. November 2021, Constructions of n-cluster tilting subcategories, Algebra seminar, Norwegian University of Science and Technology.

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

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

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

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

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

11. May 2017, An introduction to higher dimensional Auslander–Reiten theory, Mini-Conference for PhD-Students in Mathematics, Stockholm University.

12. November 2016, Colouring the Auslander–Reiten quiver of a Nakayama algebra, PhD Seminar, Uppsala University.

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

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

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

Future

Past

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 Universidad 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 (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, Winter School "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.

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.

Main lecturer

1. Rings and  modules (2023), NTNU.

2. Galois theory (2024, 2023), NTNU.

3. Homological algebra (2022), NTNU (substituting 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 Peter Soelberg: Triangulated structure of stable Frobenius categories and derived abelian categories (2024), NTNU.

2. 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.

1. September 2023–August 2024, Algebra seminar of the NTNU algebra group, organised together with Mads Sandøy.  

2. March 2020,  Uppsala Ph.D. Mathematics Conference (member of the organising committee) , Uppsala University.

1. September 2024, Researchers' Night 2024, NTNU, topic: "Explore whimsical games". Together with three colleagues we introduced to high school students three versions of Tic-Tac-Toe inspired by different mathematical concepts.

2. September 2023, Researchers' Night 2023, NTNU, topic: "What is the shape of a bubble?". I designed a poster and together with four colleagues we had a stand with a minimal surface soap bubble experiment for high school students to try.

3. September 2023, Hyfer festival, NTNU, topic: ''The art of mathematics''. Together with 4 colleagues we gave a series of talks on different topics exploring the connection between mathematics, creativity and art.

4. September 2022, Researchers' Night 2022, NTNU, topic: "The world's most difficult equation''. I designed two posters and together with two colleagues we had a stand where we were visited by and discussed with high school students.