Igor Burban

In April 2012 I have moved to Köln. My new web page is here

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

Teaching

• Lecture "Singularity Theory: Surface Singularities" , WS 2011
• Seminar "Triangulated Categories of Singularities-II" , WS 2011
• Seminar S4A1 "Triangulated Categories of Singularities" , SS 2011
• Lecture "Matrix problems and categorical constructions" , WS 2010
• Vorlesung Lineare Algebra II an der Heinrich-Heine Universität Düsseldorf, SS2010
• Lecture "Cohen-Macaulay modules over surface singularities" , WS 2009
• Hauptseminar "Elemente der klassischen homologischen Algebra" , WS 2009
• Lecture "Introduction to Hall algebras" , WS 2008
• Seminar "Tilting Theory" , SS 2008
• Lecture "Introduction to derived and triangulated categories" , WS 2007

Current PhD students

• Wassilij Gnedin
• Martin Kalck

Current Master Students

• Lennart Galinat

Former PhD Students

• Thilo Henrich, Vector bundles on degenerations of elliptic curves and Yang-Baxter equations.

Former Diploma Students

• Wassilij Gnedin, Indecomposable representations of the Gelfand quiver.
• Michael Adler, Hall Algebren und perpendikuläre Kategorien.

Former Bachelor Students

• Lennart Galinat, Injektive Moduln über Noetherschen Ringen.
• Ronja Reese, Darstellungen der Kleinschen Vierer-Gruppe über einem Körper der Charakteristik zwei.
• Christian Reineke, Morita-Äquivalenzen und ein Satz von Gabriel.
• Charlotte Ricke, Spiegelungsfunktoren und Darstellungen von ADE Köchern.
• John Schmid, Drei Beschreibungen des Bifunktors Ext^n.

Recent preprints

• I.Burban, M.Kalck, Singularity category of a non-commutative resolution of singularities (pdf), arXiv:1103.3936.
• I.Burban, Yu.Drozd, Maximal Cohen-Macaulay modules over non-isolated surface singularities (pdf), arXiv:1002.3042.

Recently accepted papers

• I.Burban, Frobenius morphism and vector bundles on cycles of projective lines (pdf), arXiv:1010.0399, to appear in Comm. in Algebra.
• 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), arXiv:0708.1685, to appear in Memoirs of the AMS.
• 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), arXiv:0903.4828, to appear in Glasgow Journal of Math.
• I.Burban, O.Schiffmann, On the Hall algebra of an elliptic curve I (pdf), math.AG/0505148, to appear in Duke Math. J.

Lecture Notes

• Coherent sheaves on an elliptic curve (pdf), Notes of Kristian Bruening of my lecture course given at Tsinghua University in August 2005, Beijing, China.
• Du Val Singularities (pdf)
• Maximal Cohen-Macaulay modules over quotient surface singularities (pdf). These are notes of my talks given in Paderborn and Osaka in 2009.