@unpublished{63620,
  abstract     = {{We introduce a new class of reflection groups associated with the canonical bilinear lattices of Lenzing, which we call reflection groups of canonical type. The main result of this work is a categorification of the corresponding poset of non-crossing partitions for any such group, realized via the poset of thick subcategories of the category of coherent sheaves on an exceptional hereditary curve generated by an exceptional sequence. A second principal result, essential for the categorification, is a proof of the transitivity of the Hurwitz action in these reflection groups.}},
  author       = {{Baumeister, Barbara and Burban, Igor and Neaime, Georges and Schwabe, Charly Merlin}},
  booktitle    = {{arXiv:2512.01729}},
  title        = {{{Non-crossing partitions for exceptional hereditary curves}}},
  year         = {{2025}},
}

@article{44328,
  abstract     = {{In this paper, we study equivalences between the categories of quasi–coherent sheaves on non–commutative noetherian schemes. In particular, we give a new proof of Căldăraru's conjecture about Morita equivalences of Azumaya algebras on noetherian schemes. Moreover, we derive necessary and sufficient condition for two reduced non–commutative curves to be Morita equivalent.}},
  author       = {{Burban, Igor and Drozd, Yu.}},
  journal      = {{Advances in Mathematics}},
  title        = {{{Morita theory for non-commutative noetherian schemes}}},
  doi          = {{10.1016/j.aim.2022.108273}},
  volume       = {{399}},
  year         = {{2022}},
}

@unpublished{44537,
  author       = {{Burban, Igor and Alfes-Neumann, C. and Raum, M.}},
  title        = {{{A classification of polyharmonic Maa forms via quiver representations}}},
  year         = {{2022}},
}

@article{44327,
  author       = {{Burban, Igor and Peruzzi, A.}},
  journal      = {{Journal of Geometry and Physics}},
  title        = {{{On elliptic solutions of the associative Yang-Baxter equation}}},
  volume       = {{176}},
  year         = {{2022}},
}

@article{44329,
  abstract     = {{This paper is devoted to algebro-geometric study of infinite dimensional Lie bialgebras, which arise from solutions of the classical Yang–Baxter equation. We regard trigonometric solutions of this equation as twists of the standard Lie bialgebra cobracket on an appropriate affine Lie algebra and work out the corresponding theory of Manin triples, putting it into an algebro-geometric context. As a consequence of this approach, we prove that any trigonometric solution of the classical Yang–Baxter equation arises from an appropriate algebro-geometric datum. The developed theory is illustrated by some concrete examples.}},
  author       = {{Burban, Igor and Abedin, R.}},
  journal      = {{Communications in Mathematical Physics}},
  number       = {{2}},
  pages        = {{1051–1109}},
  title        = {{{Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation}}},
  doi          = {{10.1007/s00220-021-04188-7}},
  volume       = {{387}},
  year         = {{2021}},
}

@article{44331,
  abstract     = {{In this paper, we study properties of the algebras of planar quasi-invariants. These algebras are Cohen–Macaulay and Gorenstein in codimension one. Using the technique of matrix problems, we classify all Cohen–Macaulay modules of rank one over them and determine their Picard groups. In terms of this classification, we describe the spectral modules of the planar rational Calogero–Moser systems. Finally, we elaborate the theory of the algebraic inverse scattering method, providing explicit computations of some ‘isospectral deformations’ of the planar rational Calogero–Moser system in the case of the split rational potential.}},
  author       = {{Burban, Igor and Zheglov, A.}},
  journal      = {{Proceedings of the London Mathematical Society}},
  number       = {{4}},
  pages        = {{1033–1082}},
  title        = {{{Cohen-Macaulay modules over the algebra of planar quasi-invariants and Calogero-Moser systems}}},
  doi          = {{10.1112/plms.12341}},
  volume       = {{121}},
  year         = {{2020}},
}

@article{44333,
  abstract     = {{This work deals with an algebro–geometric theory of solutions of the classical Yang–Baxter equation based on torsion free coherent sheaves of Lie algebras on Weierstraß cubic curves.}},
  author       = {{Burban, Igor and Galinat, L.}},
  journal      = {{Communications in Mathematical Physics}},
  number       = {{1}},
  pages        = {{123–169}},
  title        = {{{Torsion free sheaves on Weierstraß cubic curves and the classical Yang-Baxter equation}}},
  doi          = {{10.1007/s00220-018-3172-2}},
  volume       = {{364}},
  year         = {{2018}},
}

@unpublished{44538,
  author       = {{Burban, Igor and Drozd, Yu.}},
  title        = {{{Non-commutative nodal curves and derived tame algebras}}},
  year         = {{2018}},
}

@article{44332,
  author       = {{Burban, Igor and Zheglov, A.}},
  journal      = {{International Journal of Mathematics}},
  number       = {{10}},
  title        = {{{Fourier-Mukai transform on Weierstraß cubics and commuting differential operators}}},
  volume       = {{29}},
  year         = {{2018}},
}

@book{44337,
  author       = {{Burban, Igor and Drozd, Yu.}},
  isbn         = {{978-1-4704-2537-1}},
  title        = {{{Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems}}},
  doi          = {{10.1090/memo/1178}},
  volume       = {{248}},
  year         = {{2017}},
}

@unpublished{44539,
  author       = {{Burban, Igor and Drozd, Yu.}},
  title        = {{{On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems}}},
  year         = {{2017}},
}

@article{44334,
  author       = {{Burban, Igor and Galinat, L.}},
  journal      = {{Journal of Physics A: Mathematical and Theoretical}},
  title        = {{{Simple vector bundles on a nodal Weierstraß cubic and quasi-trigonometric solutions of CYBE}}},
  volume       = {{50}},
  year         = {{2017}},
}

@article{44335,
  author       = {{Burban, Igor and Drozd, Yu. and Gavran, V.}},
  journal      = {{European Journal of Mathematics}},
  number       = {{2}},
  pages        = {{311–341}},
  title        = {{{Minors of non-commutative schemes}}},
  volume       = {{3}},
  year         = {{2017}},
}

@article{44336,
  author       = {{Burban, Igor and Drozd, Yu. and Gavran, V.}},
  journal      = {{International Mathematics Research Notices 2017}},
  number       = {{3}},
  pages        = {{895--920}},
  title        = {{{Singular curves and quasi–hereditary algebras}}},
  year         = {{2017}},
}

@article{44339,
  author       = {{Burban, Igor and Gnedin, W.}},
  journal      = {{Journal of Pure and Applied Algebra}},
  number       = {{12}},
  pages        = {{3777–3815}},
  title        = {{{Cohen-Macaulay modules over some non-reduced curve singularities}}},
  volume       = {{220}},
  year         = {{2016}},
}

@article{44340,
  author       = {{Burban, Igor and Henrich, T.}},
  journal      = {{Journal of the European Math. Society}},
  number       = {{3}},
  pages        = {{591– 644}},
  title        = {{{Vector bundles on plane cubic curves and the classical Yang-Baxter equation}}},
  doi          = {{10.4171/JEMS/512}},
  volume       = {{17}},
  year         = {{2015}},
}

@article{44341,
  author       = {{Burban, Igor and Kreußler, B.}},
  journal      = {{Mathematische Nachrichten}},
  number       = {{2–3}},
  pages        = {{173–183}},
  title        = {{{Analytic moduli spaces of simple sheaves on families of integral curves}}},
  volume       = {{287}},
  year         = {{2014}},
}

@article{44342,
  author       = {{Burban, Igor and Schiffmann,  O.}},
  journal      = {{Journal für Reine und Angew. Mathematik}},
  pages        = {{75–124}},
  title        = {{{Composition algebra of a weighted projective line}}},
  volume       = {{679}},
  year         = {{2013}},
}

@book{44346,
  author       = {{Burban, Igor and Kreußler, B.}},
  isbn         = {{978-0-8218-7292-5}},
  title        = {{{Vector bundles on degenerations of elliptic curves and Yang-Baxter equations}}},
  doi          = {{10.1090/S0065-9266-2012-00654-X}},
  volume       = {{220}},
  year         = {{2012}},
}

@article{44344,
  author       = {{Burban, Igor and Schiffmann, O.}},
  journal      = {{Duke Mathematical Journal}},
  number       = {{7}},
  pages        = {{1171–1231}},
  title        = {{{On the Hall algebra of an elliptic curve I}}},
  doi          = {{10.1215/00127094-1593263}},
  volume       = {{161}},
  year         = {{2012}},
}