Publications

 

  • [BBGTY] Infinite friezes of affine type D, arXiv:2407.11232v1, (Karin Baur, L ́ea Bittmann, Emily Gunawan, Gordana Todorov, Emine Yildirim), (submitted)
  • [STZ] Defect Invariant Nakayama Algebras, arXiv:2406.00254v1, (Emre Sen, Gordana Todorov, Shijie Zhu)
  • [IT16] Which Cluster Categories are CAT(0), arXiv:2203.16679, (with K. Igusa), (submitted)
  • [HIKT] Infinitesimal semi-invariant pictures and co-amalgamation (with Eric J. Hanson, Kiyoshi Igusa, Moses Kim), arXiv:2012.06572, (2023), J. London Math. Soc. Volume109, Issue1, January 2024, https://doi.org/10.1112/jlms.12786.
  • [BCJKT] Infinite friezes and triangulations of annuli, (with Karin Baur, Ilke Canakci, Karin M. Jacobsen, Maitreyee Kulkarni), arXiv:2007.09411, Journal of Algebra and its Applications 23 (12), 2450207.
  • [IRT20] Continuous Quivers of Type A (III), Embeddings of Cluster Theories, (with Kiyoshi Igusa, Job D. Rock), arXiv:2004.10740v1, Nagoya Math. J., (2022), 1-37, DOI 10.1017/nmj.2021.16
  • [IRT] Continuous quivers of type A(I), foundations, (with Kiyoshi Igusa, Job Rock), arXiv:1909.10499, Rendiconti del Circolo Matematico di Palermo Series 2 https://doi.org/10.1007/s12215-021-00691-x, Published online January 2022.
  • [IT14] Picture groups and maximal green sequences, (with Kiyoshi Igusa), arXiv:200720, AIMS Journals, Electronic Research Archive, (2021), 29 (5) : 3031-3068. doi: 10.3934/era.2021025).
  • [BTZ] Dynamical Combinatorics and Torsion Classes, (with Emily Barnard and Shijie Zhu), arXiv:1911.10712v1, Journal of Pure and Applied Algebra 225 (2021), 106642.
  • [BFGST18b] Friezes satisfying higher Slk-determinants, (with Karin Baur, Eleonore Faber, Sira Gratz, Khrystyna Serhiyenko), arXiv:1810.10562v1, Algebra and Number Theory 15:1(2021), p.29-68.
  • [IT19] Cyclic posets and triangulation clusters, (with Kiyoshi Igusa), arXiv:1903.04318. Sci. China Math, July 2019, Vol.62, No.7: 1289-1316.
  • [BFGST17] Conway-Coxeter Friezes and Mutation: A Survey, (with Karin Baur, Eleonore Faber, Sira Gratz, Khrystyna Serhiyenko), arXiv:1806.06441. In Association for Women in Mathematics Research Symposium, pp. 47-68. Springer, Cham, 2017.
  • [NRTZ] Dominant Dimension and Tilting Modules, (with Van Nguyen, Idun Reiten and Shijie Zhu), arXiv:1706.00475v2, Mathematische Zeitschrift, (2019), 292(3), 947-973.
  • [NTZ] Preprojective algebras of tree-type quivers, (with Van Nguyen and Shijie Zhu), arXiv: 1612.01585. Communi- cations in Algebra (2019), 47 (1), 252-275.
  • [BFGST18a] Mutation of An friezes, (with Karin Baur, Eleonore Faber, Sira Gratz, Khrystyna Serhiyenko), arXiv: 1612.05374. Bulletin des Sciences Mathematiques (2018), 142, 1-48.
  • [BHIT] Semi-invariant pictures and two conjectures about maximal green sequences. (with Thomas Brustle, Stephen Hermes and Kiyoshi Igusa), arXiv:1503.07945. Journal of Algebra 473 (2017) 80-109.
  • [IOTW3] Modulated semi-invariants, (with Kiyoshi Igusa, Kent Orr and Jerzy Weyman), arxiv: 1507.03051. [IOTW4] Picture groups of finite type and cohomology in type An, (with Kiyoshi Igusa, Kent Orr and Jerzy Weyman), arXiv:1609.02636v1.
  • [IT15] Continuous Cluster Categories II; Continuous Cluster-Tilted Categories, (with Kiyoshi Igusa), arXiv:1909.05340
  • [IT13] Signed exceptional sequences, (with Kiyoshi Igusa), arXiv:1706.02041v1.
  • [ITW] Periodic trees and semi-invariants, (with Kiyoshi Igusa, Jerzy Weyman) arXiv1407.0619.
  • [IT12] Continuous cluster categories of type D, (with Kiyoshi Igusa), arXiv:1309.7409.
  • [IRTT] Lattice structure of torsion classes for path algebras, (with Osamu Iyama, Idun Reiten, Hugh Thomas), arXiv:1312.3659. Bull. London Math. Soc. (2015) 47 (4): 639-650.
  • [IT11] Cluster categories coming from cyclic posets, (with Kiyoshi Igusa), ArXiv:1303.6697, Communications in Algebra, Vol. 43, (2015), pp 4367-4402.
  • [IT10] Continuous Cluster Categories I, (with Kiyoshi Igusa), arXiv:1209.1879, Algebras and Representation Theory, Vol.18, (2015), pp.65-101.
  • [IT9] Continuous Frobenius categories, (with Kiyoshi Igusa), arXiv:1209.0038. Abel Symposia, Volume 8, (2013), Algebras, Quivers and Representations, The Abel Symposium 2011.
  • [BBT] Projective dimension of modules over cluster-tilted algebras. (with Louis Beaudet, Thomas Brustle), arXiv:1111.2013, Algebras and Representation Theory, December 2014, Volume 17, Issue 6, pp 1797-1807: doi.org/10.1007/s10468-014-9472-0
  • [AIRT] Preprojective algebras and c-sortable words. (with Claire Amiot, Osamu Iyama, Idun Reiten), arXiv:1002.4131, Proc. London Math. Soc. 103(4)(2011)
  • [ART] The ubiquity of generalized cluster categories. (with Claire Amiot, Idun Reiten), arXiv:0911.4819, Adv. Math., 226 (2011), pp. 3813-3849.
  • [Tod] Cluster Categories and their relation to Cluster Algebras, Semi-invariants and Homology of torsion free nilpotent groups. Volumen 48, numero 3 (2007) pag. 27-52 Revista de la Union Matematica Argentina.
  • [IOTW] Cluster complexes via Semi-invariants. (with K. Igusa, K.Orr, J. Weyman), ArXiv:math. 0708.0798, Com- positio Mathematica (2009), 145 : 1001-1034.
  • [To] Cluster Categories and their Relation to Cluster Algebras, Semi- invariants. Milan Journal of Mathematics, 76 (2007), 1-28.
  • [ABST2] m-cluster categories and m-replicated algebras. (with I. Assem, T. Bruestle, R. Schiffler), ArXiv:math.RT/0608727, Journal of Pure and Applied Algebra, 212(2008), 884-901.
  • [ABST1] Cluster categories and duplicated algebras., (with I. Assem, T. Brustle, R. Schiffler), J. of Algebra 305 (2006) 548-561.
  • [BMRT] Clusters and seeds in acyclic cluster algebras. (with A. B. Buan, R. J. Marsh, I. Reiten), Includes appendix co-authored by P. Caldero and B. Keller. Proc. Amer. Math. Soc. 135, No. 10 (2007), 3049-3060.
  • [BMRRT] Tilting theory and cluster combinatorics. (with A. B. Buan, R. J. Marsh, M. Reineke, I. Reiten), Adv. Math. 204 (2006), 572-618. (”Fast Breaking Paper” in October 2007, Essential Science Indicators from Thomson Scientific.)
  • [IT8] On the finitistic global dimension conjecture for Artin algebras. Representations of algebras and related topics, 201–204, Fields Inst. Commun., 45, Amer. Math. Soc., Providence, RI, 2005. (with K.Igusa)
  • [TY] Locally finitely presented bifunctors. Representation theory of algebras (Cocoyoc, 1994), 659–670, CMS Conf. Proc., 18, Amer. Math. Soc., Providence, RI, 1996. (with R.Yang)
  • [GT2] Extensions, kernels and cokernels of homologically finite subcategories. Representation theory of algebras (Cocoyoc, 1994), 227–235, CMS Conf. Proc., 18, Amer. Math. Soc., Providence, RI, 1996. (with R.Gentle)
  • [GT1] Approximations, adjoint functors and torsion theories. Representations of algebras (Ottawa, ON, 1992), 205– 219, CMS Conf. Proc., 14, Amer. Math. Soc., Providence, RI, 1993. (with R.Gentle)
  • [APT] Homological theory of idempotent ideals. Trans. Amer. Math. Soc. 332 (1992), no. 2, 667–692. (with M.Auslander, M.I.Platzeck)
  • [TZ] Remarks on Auslander algebras. J. Pure Appl. Algebra 70 (1991), no. 3, 307–314. (with D.Zacharia)
  • [IST] Finite projectivity and contravariant finiteness. Proc. Amer. Math. Soc. 109 (1990), no. 4, 937–941. (with K.Igusa, S.O.Smalo)
  • [IT6] Tits form numbers. Comm. Algebra 17 (1989), no. 9, 2197–2222. (with K.Igusa)
  • [IPTZ] Auslander algebras of finite representation type. Comm. Algebra 15 (1987), no. 1-2, 377–424. (with K.Igusa, M.I.Platzeck, D.Zacharia)
  • [IT5] A numerical characterization of finite Auslander-Reiten quivers. Representation theory, I (Ottawa, Ont., 1984), 181–198, Lecture Notes in Math., 1177, Springer, Berlin, 1986. (with K.Igusa)
  • [BT] On a theorem of Nazarova and Ro ̆ıter. Representation theory, I (Ottawa, Ont., 1984), 50–54, Lecture Notes in Math., 1177, Springer, Berlin, 1986. (with O.Bretscher)
  • [IT4] Preprojective partitions and the determinant of the Hom matrix. Proc. Amer. Math. Soc. 94 (1985), no. 2, 189–197. (with K.Igusa)
  • [IT3] A characterization of finite Auslander-Reiten quivers. J. Algebra 89 (1984), no. 1, 148–177. (Reviewer: Sheila Brenner) 16A64 (16A62) (with K.Igusa)
  • [IT2] Radical layers of representable functors. J. Algebra 89 (1984), no. 1, 105–147. (with K.Igusa)
  • [T2] A note on preprojective partitions over hereditary Artin algebras. Proc. Amer. Math. Soc. 85 (1982), no. 4, 523–528.
  • [PT] TrD-periodic modules over self-injective algebras. Representations of algebras (Puebla, 1980), pp. 285–301, Lecture Notes in Math., 903, Springer, Berlin-New York, 1981. (with M.I.Platzeck)
  • [T] Almost split sequences for TrD-periodic modules. Representation theory, II (Proc. Second Internat. Conf., Car- leton Univ., Ottawa, Ont., 1979), pp. 600–631, Lecture Notes in Math., 832, Springer, Berlin, 1980.

 

BOOKS EDITED

  • [IMT4] Igusa K., Martsinkovsky A., Todorov G., editors, Representations of Algebras, Geometry and Physics, Con- temporary Mathematics, 769, 2021.
  • [IMT3] Igusa K., Martsinkovsky A., Todorov G., editors, Surveys in Representation Theory, Contemporary Mathe- matics, 716, 2018.
  • [IMT2] Igusa K., Martsinkovsky A., Todorov G., editors, Recent Developments in Representation Theory, Contem- porary Mathematics, 673, 2016.
  • [IMT1] Igusa K., Martsinkovsky A., Todorov G., editors, Expository Lectures on Representation Theory, Contempo- rary Mathematics, 607, 2014.
  • [MT] Representation theory and algebraic geometry. Papers from the Memorial Conference for Maurice Auslander held at Brandeis University, Waltham, MA, March 24–26, 1995. Edited by A. Martsinkovsky and G. Todorov. London Mathematical Society Lecture Note Series, 238. Cambridge University Press, Cambridge, 1997. viii+123 pp. ISBN: 0-521-57789-6 16-06 (00B25 00B30