Homological Algebra, derived and triangulated categories
Homological Mirror Symmetry
Fourier-Mukai Transforms
Vector bundles on singular curves
Representation theory of associative algebras
Ringel-Hall Algebras
Cohen-Macaulay Modules
Preprints
I.Burban, Yu.Drozd, Maximal Cohen-Macaulay modules over surface singularities
(pdf), arXiv:0803.0117
I.Burban, B.Kreussler, Vector bundles on degenerations of elliptic curves and Yang-Baxter equations
(pdf),
arXiv:0708.1685
I.Burban, O.Schiffmann, On the Hall algebra of an elliptic curve I
(pdf),
math.AG/0505148
Publications in Mathematical Journals
I.Burban, O.Iyama, B.Keller, I.Reiten, Cluster tilting
for one-dimensional hypersurface singularities
(pdf),
Adv. Math. vol. 217, no 6, 2443-2484 (2008), see also arXiv:0704.1249.
I.Burban, B.Kreussler, Derived categories of irreducible projective
curves of arithmetic genus one (pdf),
Compositio Math. vol. 142 1231-1262 (2006), see also math.AG/0503496
I.Burban, B.Kreussler,
On a relative Fourier-Mukai transform on genus one fibrations
(pdf),
Manuscr. Math., vol. 120, no. 3, 283-306 (2006), see also math.AG/0410349
I.Burban, B.Kreussler,
Fourier-Mukai transforms and semi-stable sheaves on nodal Weierstrass cubics
(pdf),
J. Reine Angew. Math., vol. 584, 45-82, (2005), see also math.AG/0401437
I.I.Burban, I.M.Burban,
Derived Categories and D-Branes (in Ukrainian) (ps),
Ukrain. Mat. Zh., vol. 57, no. 1, 18-31 (2005)
I.Burban, Yu.Drozd,
Coherent sheaves on rational curves with simple double points and
transversal intersections
(ps),
Duke Math. J., vol. 121, no. 2, 189-229 (2004)
I.Burban, Yu.Drozd,
Derived tameness of nodal algebras (pdf),
Journal of
Algebra, vol. 272, no. 1, 46-94, (2004), see also math.RT/0307060
I.Burban, Stable vector bundles on a rational curve with one node (in Ukrainian)
(ps),
Ukrain. Mat. Zh., vol. 55, no. 7, 867-874 (2003)
I.Burban, H.-G.Freiermuth,
Geometrical properties of sections of Buchsbaum-Rim sheaves
(pdf),
Le Matematiche, vol. LVII 265-283, (2002), see also math.AG/0010276
Publications in Conference Proceedings
L.Bodnarchuk, I.Burban, Yu.Drozd, G.-M.Greuel,
Vector bundles and torsion free sheaves on degenerations of
elliptic curves (pdf),
Global Aspects of Complex Geometry, 83-129, Springer, (2006), see also math.AG/0603261
I.Burban, Yu.Drozd, Derived categories for nodal rings and projective
configurations (pdf), Noncommutative Algebra and Geometry,
A series of Lecture Notes in Pure and Applied Mathematics, vol. 243, 23-46 (2005)
I.Burban, Yu.Drozd, Indecomposables of the derived categories of certain associative
algebras
(pdf),
Proceedings of the ICRA-X Conference,
Toronto 2002, Fields Institute Communications, vol. 45, 109-127 (2004), see also math.RT/0307062
I.Burban, Derived categories of coherent sheaves on rational
singular curves (pdf),
Representations of finite dimensional algebras and related topics in
Lie theory and geometry, 173-188, Fields Inst. Commun., vol. 40,
Amer. Math. Soc., Providence, RI, 2004
I.Burban, Yu.Drozd, Derived categories and matrix problems, Proceedings of the
Third International Algebraic Conference in Ukraine, 201--211, (2002),
Kiev Institute of Mathematics of the
National Academy of Sciences.
I.Burban, Yu.Drozd, G.-M.Greuel, Vector bundles on singular projective curves
(ps),
Applications of algebraic geometry to coding theory,
physics and computation, Proceedings of the NATO advanced research workshop, Eilat, Israel,
February 25-March 1, 2001, Kluwer Academic Publishers, 1-15 (2001)
PhD Thesis: Abgeleitete Kategorien und Matrixprobleme (ps)
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