Publications

Books

  1. G. Leuschke, F. Bleher, R. Schiffler and D. Zacharia : Representations of Algebras, AMS Contemp. Math. Volume 705, 2018.
  2. R. Schiffler : Quiver Represenations, CMS Books in Mathematics, Springer Verlag, 2014.
    There is a book review on page 7 of these CMS Notes.
  3. R. Schiffler : Variétés de carquois et homologie d’intersection , Publications LACIM 30, Montréal, 2003.

Lecture Notes

  1. R. Schiffler : Lecture notes on cluster algebras from surfaces, CIMPA School, Mar del Plata, 2016, in I. Assem and S. Trepode (editors) Homological Methods, Representation Theory, and Cluster Algebras, CRM Short Courses, Springer, 2018.
  2. R. Schiffler : Cluster algebras and cluster categories, lecture notes for the Latin American Colloquium, Sao Pedro, Brazil, 2009.

Articles

  1. T. Brüstle, E. J. Hanson, S. Roy and R. Schiffler, An exact structure approach to almost rigid modules over quivers of type A, preprint, 15 pages.
  2. V. Bazier-Matte and R. Schiffler, Knot theory and cluster algebras III: Posets, preprint, 49 pages.
  3. E. Barnard, R. Coelho-Simões, E. Gunawan and R. Schiffler, Maximal almost rigid modules over gentle algebras, preprint, 50 pages.
  4. A. Burcroff, N. Ovenhouse, R. Schiffler and S. Zhang, Higher $q$-continued fractions, preprint, 23 pages.
  5. V. Bazier-Matte and R. Schiffler, Knot theory and cluster algebras II: The knot cluster, preprint, 49 pages.
  6. G. Musiker, N. Ovenhouse, R. Schiffler and S. Zhang, Higher dimer covers on snake graphs, preprint, 31 pages.
  7. B. Duan and R. Schiffler, Real simple modules over simply-laced quantum affine algebras and categorifications of cluster algebras, preprint, 101 pages.
  8. R. Schiffler and K. Serhiyenko, A geometric model for syzygies over 2-Calabi-Yau tilted algebras, 107 pages.
  9. K. Baur, B. Marsh, R. Schiffler, and S. Schroll (Editors) Oberwolfach Reports 21 (1), 69-136 (2024).
  10. R. Schiffler and K. Serhiyenko, On Gorenstein algebras of finite Cohen-Macaulay type: dimer tree algebras and their skew group algebras, J. Algebra 660, (2024) 91-133.
  11. R. Schiffler, Perfect matching problems in cluster algebras and number theory, in AMS Proceedings of Symposia in Pure Mathematics Volume: 110; (2024).
  12. R. Schiffler and K. Serhiyenko, A geometric model for syzygies over 2-Calabi-Yau tilted algebras II, IMRN, rnad078, (2023), 32 pages.
  13. K. Lee, L. Li, M. Rabideau and R. Schiffler, On the ordering of the Markov numbers,  Adv. Appl. Math. 143 (2023), 102453
  14. E. Barnard, E. Gunawan, E. Meehan and R. Schiffler, Cambrian combinatorics on quiver representations (type A),  Adv. Appl. Math. 143, (2023), 102428
  15. V. Bazier-Matte and R. Schiffler, Knot theory and cluster algebras, Adv. Math. 408  B, (2022), 108609.
  16. R. Schiffler and D. Whiting, Tilting modules arising from knot invariants,  J. Pure Appl. Alg. 226 (2022) 107041.
  17. I. Assem, M. J. Redondo and R. Schiffler, A note on sequential walks, Contemp. Math. 761 (2021) 37-50. 
  18. K. Igusa and R. Schiffler, Frieze varieties are invariant under Coxeter mutation, Contemp. Math. 761 (2021) 103-116.
  19. K. Lee, L. Li and R. Schiffler, Newton polytopes of rank 3 cluster variables,  Algebraic Combinatorics, 3 (2020) no. 6, 1293-1330.
  20. B. Duan and R. Schiffler, A geometric q-character formula for snake modules,  J. Lond. Math. Soc. (2) 102 (2020) 846–878.
  21. M. Rabideau and R. Schiffler, Continued fractions and orderings on the Markov numbers, Adv. Math.  370, 26 (2020), Article 107231.
  22. E. Gunawan and R. Schiffler, Frieze vectors and unitary friezes,  J. Comb. 11, 4, 681–703 (2020).
  23. H. Gao and R. Schiffler, On the number of support $\tau$-tilting modules over Nakayama algebras, SIGMA 16 (2020), 058, 13 pages.
  24. R. Schiffler and Robinson-Julian Serna, A geometric realization of socle-projective categories for posets of type A,  J. Pure Appl. Alg.  224,  12 (2020) Article 106436.
  25. K. Lee, L. Li, M. Mills, R. Schiffler and A. Seceleanu,  Frieze varieties : A characterization of the finite-tame-wild trichotomy for acyclic quivers,  Adv. Math. 367 (2020) Article 107130.
  26. I. Canakci and  R. Schiffler, Snake graphs and continued fractions,  European J. Comb. Volume 86 (2020).
  27. W. Chang and R. Schiffler Cluster automorphisms and quasi-automorphisms, Adv. Appl. Math. 110 C (2019) 342-374.
  28. K. Lee and  R. Schiffler, Cluster algebras and Jones polynomials, Sel. Math. New Ser. (2019) 25: 58.
  29. R. Schiffler Snake graphs, perfect matchings and continued fractions. Snapshots of modern mathematics from Oberwolfach, (2019).
  30. C. Paquette and  R. Schiffler, Group actions on cluster algebras and cluster categories, Adv. Math.  345, (2019) 161-221.
  31. I. Assem, M.A. Gatica and R. Schiffler, Hochschild cohomology of partial relation extension algebras, Comm. Alg. 46, (2018) Issue 12.
  32. R. Schiffler, Cluster algebras arising from surfaces, Homological Methods, Representation Theory, and Cluster Algebras, CRM Short Courses, Springer, 2018.
  33. I. Canakci and  R. Schiffler, Cluster algebras and continued fractions, Compos. Math. 154 (3) (2018) 565-593.
  34. I. Assem, R. Schiffler and  K. Serhiyenko, Modules over cluster-tilted algebras that do not lie on local slices, Archiv Math. 110, (2018) 9-18.
  35. R. Schiffler and  K. Serhiyenko, Injective presentations of induced modules over cluster-tilted algebras, Algebras and Represent. Theory 21, 2, (2018) 447-470.
  36. I. Assem, R. Schiffler and  K. Serhiyenko, Cluster-tilted and quasi-tilted algebras, J. Pure Appl. Alg. 221, 9, (2017) 2266-2288.
  37. I. Canakci and R. Schiffler, Snake graph calculus and cluster algebras from surfaces III: Band graphs and snake rings, Int. Math. Res. Not. rnx157 (2017) 1-82.
  38. R. Schiffler and  K. Serhiyenko, Induced and coinduced modules over cluster-tilted algebras, J. Algebra 472 (2017), 226-258.
  39. A. Garcia Elsener and R. Schiffler, On syzygies over 2-Calabi-Yau tilted algebras, J. Algebra 470 (2017), 91-121.
  40. R. Schiffler, Lecture notes on cluster algebras, by Robert J. Marsh, book review, Bull. Amer. Math. Soc. 53 (2016), 325-330.
  41. I. Assem, M. A. Gatica, R. Schiffler, and R. Taillefer, Hochschild cohomology of relation extension algebras, J. Pure Appl. Alg. 220, 7, (2016), 2471–2499.
  42. I. Canakci, K. Lee and R. Schiffler, On cluster algebras from unpunctured surfaces with one marked point, Proc. Amer. Math. Soc Ser. B 2 (2015) 35-49.
  43. I. Assem, M. J. Redondo and R. Schiffler, On the first Hochschild cohomology group of a cluster-tilted algebra, Algebr. Represent. Theory 18 (6), (2015), 1547-1576.
  44. I. Canakci and R. Schiffler, Snake graph calculus and cluster algebras from surfaces II: Self-crossing snake graphs, Math. Z. 281 (1), (2015), 55-102.
  45. K. Lee and R. Schiffler, Positivity for cluster algebras, Ann. Math. 182 (1), (2015) 73-125.
  46. I. Assem, V. Shramchenko and R. Schiffler, Addendum to Cluster automorphisms and compatibility of cluster variables, Glasgow Math. J. 56 (3), (2014).
  47. I. Assem, V. Shramchenko and R. Schiffler, Cluster automorphisms and compatibility of cluster variables, Glasgow Math. J. 56 (3), (2014) 705-720.
  48. K. Lee and R. Schiffler, Positivity for cluster algebras of rank 3, Publ. Res. Inst. Math. Sci. 49, (2013) 601-649.
  49. I. Assem, G. Dupont and R. Schiffler, On a category of cluster algebras, J. Pure Appl. Alg. 218 (3), (2013) 553-582.
  50. I. Canakci and R. Schiffler, Snake graph calculus and cluster algebras from surfaces, J. Algebra, 382, (2013) 240-281.
  51. I. Assem, J. C. Bustamante, K. Igusa and R. Schiffler, The first Hochschild cohomology group of a cluster-tilted algebra revisited, Internat. J. Algebra Comput. 23 (4), (2013) 729-744.
  52. I. Assem, M. A. Gatica, and R. Schiffler, The higher relation bimodule, Algebras Represent. Theory, 16, 4 (2013), 979-999.
  53. G. Musiker, R. Schiffler, and L. Williams, Bases for cluster algebras form surfaces, Compos. Math 149, 2, (2013) 217-263.
  54. K. Lee, and R. Schiffler, A Combinatorial Formula for Rank 2 Cluster Variables, J. Alg. Comb. 37, 1, (2013) 67-85.
  55. K. Lee and R.Schiffler,  Proof of a positivity conjecture of M.Kontsevich on non-commutative cluster variables, Compos. Math. 148, 6, (2012) 1821-1832.
  56. M. Oryu and R. Schiffler, On one-point extensions of cluster-tilted algebras,  J. Algebra 357, (2012) 168-182.
  57. R.Kinser and R. Schiffler, Idempotents in representation rings of quivers, Algebra Number Theory 6, No. 5, (2012), 967-994.
  58. L. David-Roesler and R. Schiffler, Algebras from surfaces without punctures, J. Algebra 350, (2012), 218-244.
  59. I. Assem, G. Dupont, R. Schiffler and D. Smith, Friezes, strings and cluster variables, Glasgow Math. J. 54, 1 (2012) 27-60.
  60. I. Assem, V. Shramchenko, R. Schiffler, Cluster automorphisms, Proc. Lond. Math. Soc. 104(6),  (2012), 1271-1302.
  61. G. Musiker, R. Schiffler, and L. Williams, Positivity for cluster algebras from surfaces, Adv. Math. 227 (2011) 2241-2308.
  62. I. Assem, T.Brüstle and R. Schiffler, Cluster-tilted algebras without clusters, J. Algebra 324, (2010) 2475-2502.
  63. K. Igusa and R. Schiffler, Exceptional sequences and clusters,  J. Algebra 323, 8, (2010) 2183-2202.
  64. G. Musiker and R. Schiffler, Cluster expansion formulas and perfect matchings, J. Alg. Comb. 33, 2, (2010) 187-209.
  65. R. Schiffler: On cluster algebras arising from unpunctured surfaces II, Adv. Math. 223 (2010) 1885-1923.
  66. R. Schiffler, Cluster algebras and cluster categories, lecture notes for the Latin American Colloquium, Sao Pedro, Brazil, (2009).
  67. G. Musiker and R. Schiffler,  Cluster algebras of unpunctured surfaces and snake graphs, in DMTCS Proceedings, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009),  673-684.
  68. R. Schiffler and H. Thomas, On cluster algebras arising from unpunctured surfaces, Intern. Math. Res. Not. 17 (2009) 3160-3189.
  69. I. Assem, T. Brüstle and R. Schiffler, On the Galois covering of a cluster-tilted algebra, J. Pure Appl. Alg. 213, (7) (2009) 1450-1463.
  70. R. Schiffler, A cluster expansion formula (A_n case), Electron. J. Combin. 15 (2008) #R64 1.
  71. I. Assem,  T. Brüstle and R. Schiffler, Cluster-tilted algebras and slices, J. of Algebra 319 (2008) 3464-3479.
  72. I. Assem, T. Brüstle and R. Schiffler, Cluster-tilted algebras as trivial extensions, Bull. London Math. Soc. 40 (2008) 151-162.
  73. R. Schiffler, A geometric model for cluster categories of type D_n, J. Alg. Comb. 29, no. 1, (2008) 1-21.
  74. I. Assem,  T. Brüstle, R. Schiffler and G. Todorov, m-cluster categories and m-replicated algebras, J. Pure Appl. Alg. 212 (4) (2008) 884-901.
  75. I. Assem, T. Brüstle, R. Schiffler and G. Todorov, Cluster categories and duplicated algebras, J. of Algebra 305 (2006) 548-561.
  76. P. Caldero, F. Chapoton and R. Schiffler, Quivers with relations and cluster tilted algebras, Algebras and Representation Theory 9, no.4, (2006) 359-376.
  77. P. Caldero, F. Chapoton and R. Schiffler, Quivers with relations arising from clusters (A_n case), Trans. Amer. Math. Soc. 358 , no. 3, (2006) 1347-1364.
  78. R. Schiffler, On the multiplication in the quantized enveloping algebra of type A, in Representations of Algebras and Related Topics, Fields Institute Communications 45, (2005).
  79. P. Caldero and R. Schiffler, Rational smoothness of varieties of representations for quivers of Dynkin type, Annales de l’Institut Fourier 54 (2), (2004) 295-315.
  80. R. Schiffler, Projective rational smoothness of varieties of representations for quivers of type A, Representation Theory 7 (2003) 549-586.
  81. R. Bédard, and R. Schiffler, Rational smoothness of varieties of representations for quivers of type A, Representation Theory 7, (2003) 481-548.