Research group Algebra
Welcome to the homepage of the research group "Algebra"
Research
Aktuelle Forschungsprojekte:
- Homologische Algebra, abgeleitete und triangulierte Kategorien
- Vektorbündel und kohärente Garben auf singulären Kurven
- Ringel-Hall-Algebren und quanten affinen Algebren
- Darstellungstheorie der assoziativen Algebren
- Fourier-Mukai-Transformationen
- Cohen-Macaulay-Moduln
- Yang-Baxter-Gleichungen
Teaching
Lehre im SS 2024:
- Homologische Algebra und Garbentheorie
- Oberseminar "Algebra und Algebraische Geometrie"
- Seminar "Poisson Geometry and Integrable Systems
Lehre im WS 2023/24:
- Einführung in die Darstellungstheorie
- Lineare Algebra I
- Oberseminar "Algebra und Algebraische Geometrie"
- Seminar "Poisson Geometry and Integrable Systems"
Information about teaching in previous semesters can be found on this website.
Publications
Representation theory of the Gelfand quiver and Harish-Chandra modules for SL_2(R)
I. Burban, W. Gnedin, ArXiv:2604.00274 (2026).
Representation theory of the real Gelfand order and real Harish-Chandra modules for SL_2(R)
I. Burban, Y. Drozd, ArXiv:2605.18000 (2026).
Non-crossing partitions for exceptional hereditary curves
B. Baumeister, I. Burban, G. Neaime, C.M. Schwabe, ArXiv:2512.01729 (2025).
Algebraic Geometry of the Multilayer Model of the Fractional Quantum Hall Effect on a Torus
I. Burban, S. Klevtsov, Communications in Mathematical Physics 406 (2025).
Some aspects of the theory of nodal orders
I. Burban, Y. Drozd, in: Contemporary Mathematics, American Mathematical Society, Providence, Rhode Island, 2025.
Exceptional hereditary curves and real curve orbifolds
I. Burban, Algebra and Discrete Mathematics 38 (2025) 166–203.
Norms of wave functions for FQHE models on a torus
I. Burban, S. Klevtsov, in: Contemporary Mathematics, American Mathematical Society, Providence, Rhode Island, 2025.
Du Val Singularities
I. Burban, in: Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham, 2023.
Du Val Singularities
I. Burban, in: Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham, 2023.
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Activities
- Integral Structures in Geometry and Representation Theory - SFB/TRR 358
- Representation Theory and Non-Commutative Geometry / ARTIG 3
- Representation Theory and Triangulated Categories
- Oberseminar Algebraic Geometry and Representation Theory
- Seminar Poisson geometry and integrable systems
