Prof. Dr. Igor Burban
Research Interests
- Homological algebra, derived and triangulated categories
- Vector bundles and coherent sheaves on singular curves
- Ringel-Hall algebras and quantum affine algebras
- Representation theory of associative algebras
- Fourier-Mukai transforms
- Cohen-Macaulay modules
- Yang-Baxter equations
My group
Teaching and Seminars (Sommersemester 2013)
Teaching (Wintersemester 2012/13)
Recent preprints
- I.Burban, W.Gnedin,
Cohen-Macaulay modules over some non-reduced curve singularities
(pdf), arXiv:1301.3305.
-
I.Burban, B.Kreussler, Analytic moduli spaces of simple sheaves on families of integral curves
(pdf), arXiv:1212.5477, to appear in Mat. Nachr.
- I.Burban, T.Henrich,
Vector bundles on plane cubic curves and the classical Yang-Baxter equation
(pdf), arXiv:1202.5738.
- I.Burban, Yu.Drozd,
Maximal Cohen-Macaulay modules over non-isolated surface singularities
(pdf), arXiv:1002.3042.
Recent publications
- I.Burban, M.Kalck,
Relative singularity category of a non-commutative resolution of singularities
(pdf), Adv. in Math., vol. 231, no. 1, 414-435 (2012).
- I.Burban, Frobenius morphism and vector bundles on cycles of projective lines (pdf), Comm. in Algebra, vol. 40, no. 8, 2983-2988 (2012).
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I.Burban, Yu.Drozd,
Tilting on non-commutative rational projective curves
(pdf), Mathematische Annalen, vol. 351, no. 3, 665-709 (2011).
- I.Burban, T.Henrich,
Semi-stable vector bundles on elliptic curves and the associative Yang-Baxter equation
(pdf), Journal of
Geometry and Physics, vol. 62, no. 2, 312-329 (2012).
- I.Burban, B.Kreussler, Vector bundles on degenerations of elliptic curves and Yang-Baxter equations
(pdf),
Memoirs of the AMS, vol. 220, no. 1035 (2012).
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I.Burban, O.Schiffmann, Composition algebra of a weighted projective line
(pdf),
arXiv:1003.4412, to appear in Journal für Reine und Angew. Mathematik.
- I.Burban, O.Schiffmann, Two descriptions of the quantum affine algebra $U_v(sl^_2)$
via Hall algebra approach
(pdf),
Glasgow Mathematical Journal, vol. 54, no. 2, 283-307 (2012).
- I.Burban, O.Schiffmann, On the Hall algebra of an elliptic curve I
(pdf), Duke Math. Journal, vol. 161, no. 7, 1171-1231 (2012).
Contact
Universität zu Köln
Mathematisches Institut
Weyertal 86-90
D-50931 Köln
Germany
email: burban at math dot uni hyphen koeln dot de
Telefon: 0049 (0)221 470 3431
Sprechstunde im SS13: Freitags 14:45-15:45
Sekretariat
Frau Regina Deeg
Universität zu Köln
Mathematisches Institut
Weyertal 86-90
D-50931 Köln
Germany
email: rdeeg at math dot uni hyphen koeln dot de
Telefon: 0049-(0)221-470-5759