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At the University of Lisbon, ULisboa, I obtained the degrees of Bacharelato (1976) and of Licenciatura (1978), as well as the title of Agregado in Mathematics (2002). At the University of St Andrews, Scotland, I received the degree of Doctor of Philosophy (1983). I was a full professor since 2004 at the Faculdade de Ciências da Universidade de Lisboa, FCUL, where I started my academic career as a tutor. I retired in 2023, but continue research activities. I was a member of the Centro de Algebra, CAUL, since its beginning. There I created the research line ¿Semigroups and Languages¿, and I was the Coordinator during many years until it was extinguished. Then, I became a member of Centro de Matemática Computacional e Estocástica, CEMAT, being responsible for its polo at FCUL, until 2021. I have belonged to various committees and directive/scientific bodies at ULisboa and at FCUL. Within the scope of the FCT, I have been an evaluator of diverse applications. I have also been a member of the A3ES evaluation panel for Mathematics. I am often asked to be a promotion evaluator and member of both academic degrees and academic positions at various schools, both in Portugal and abroad. I (co-)supervised the academic work of many graduate students, in particular Master's (18) and Doctoral Theses (7), I have also guided research fellows and post-docs. The importance of the international collaboration is indisputable, and in this context, I have carried out internships abroad, promoted the visit of specialists and organized regular international scientific meetings in the areas of the Theories of Semigroups, Automata and Languages, as well as in Computer Algebra. My research work lies in the field of Semigroup Theory, studying both the structure of specific semigroups and the description of classes of semigroups. I am (co-)author of 60 papers, under the name Gracinda M. S. Gomes, having developed work in collaboration with colleagues from several Portuguese and foreign universities. I was part of the editorial board of various proceedings and have published the undergraduate book ¿Anéis e corpos ¿ uma introdução¿, Textos de Matemática, DM-FCUL. During my career I taught many different topics, mainly in the área of Algebra. I was nominated ¿Sócio Honorário¿ of the Sociedade Portuguesa de Matemática in 2022. Lisboa,February 18, 2024
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Identificação

Identificação pessoal

Nome completo
Gracinda Maria Santos Gomes Moreira da Cunha

Nomes de citação

  • M. S. Gomes, Gracinda
  • Gracinda M. S. Gomes

Identificadores de autor

Ciência ID
911A-5FA5-9D8B
ORCID iD
0000-0003-3359-7141

Endereços de correio eletrónico

  • gmcunha@fc.ul.pt (Profissional)

Moradas

  • Departamento de Matemática, FCUL, Campo Grande 016, 1749-016, Lisbon, Lisbon, Portugal (Profissional)

Websites

Domínios de atuação

  • Ciências Exatas - Matemática

Idiomas

Idioma Conversação Leitura Escrita Compreensão Peer-review
Português (Idioma materno)
Inglês Utilizador proficiente (C1) Utilizador proficiente (C1) Utilizador proficiente (C1) Utilizador proficiente (C1) Utilizador proficiente (C1)
Francês Utilizador independente (B1) Utilizador independente (B2) Utilizador independente (B2) Utilizador independente (B2) Utilizador independente (B2)
Formação
Grau Classificação
2002
Concluído
 Agregação em Matemática (Título de Agregado)
Universidade de Lisboa Faculdade de Ciências, Portugal
1984 - 1984
Concluído
 Matemática (Doutoramento)
Especialização em Algebra and Geometry
Universidade de Lisboa, Portugal
1980/10 - 1983/07
Concluído
 Mathematics (Doktor (PhD))
Especialização em Matemática, Algebra
University of St Andrews, Reino Unido
"Aspects of order and congruence relations on regular semigroups" (TESE/DISSERTAÇÃO)
1973/10 - 1978
Concluído
 Matemática (Licenciatura)
Especialização em matemática pura
Universidade de Lisboa Faculdade de Ciências, Portugal
 18
1973/10 - 1976/07
Concluído
 Matemática (Bacharelato)
Universidade de Lisboa, Portugal
 18
Percurso profissional

Docência no Ensino Superior

Categoria Profissional
Instituição de acolhimento 		Empregador
2004 - Atual Professor Catedrático (Docente Universitário) Universidade de Lisboa Faculdade de Ciências, Portugal
Projetos

Projeto

Designação Financiadores
2020/01/01 - 2023/12/31 Center for Computational and Stochastic Mathematics
UIDB/04621/2020
10.54499/UIDB/04621/2020
Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento, Portugal

Universidade de Lisboa Centro de Matemática Computacional e Estocástica, Portugal

FCiênciasID Associação para a Investigação e Desenvolvimento de Ciências, Portugal
Fundação para a Ciência e a Tecnologia
Concluído
2018/10/01 - 2022/09/30 Semigrupos: conjugação, computação, cristais e combinatória.
PTDC/MAT-PUR/31174/2017
Associação para a Inovação e Desenvolvimento da FCT, Portugal

FCiênciasID Associação para a Investigação e Desenvolvimento de Ciências, Portugal

Universidade Aberta, Portugal
Fundação para a Ciência e a Tecnologia
Concluído
2019/01/01 - 2019/12/31 Centro de Matemática Computacional e Estocástica
UID/Multi/04621/2019
Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento, Portugal

FCiênciasID Associação para a Investigação e Desenvolvimento de Ciências, Portugal

Universidade de Lisboa Instituto Superior Técnico, Portugal
Fundação para a Ciência e a Tecnologia
Concluído
2014/01/01 - 2015/02/15 Projecto Estratégico - UI 143 - 2014
PEst-OE/MAT/UI0143/2014
Fundação da Faculdade de Ciências da Universidade de Lisboa, Portugal

Universidade de Lisboa Faculdade de Ciências, Portugal
Fundação para a Ciência e a Tecnologia
Concluído
2011/01/01 - 2013/12/31 Projecto Estratégico - UI 143 - 2011-2012
PEst-OE/MAT/UI0143/2011
Fundação da Faculdade de Ciências da Universidade de Lisboa, Portugal

Universidade de Lisboa Faculdade de Ciências, Portugal
Fundação para a Ciência e a Tecnologia
Concluído
2007/07/01 - 2010/12/31 Semigrupos e Linguagens
PTDC/MAT/69514/2006
Universidade de Lisboa Faculdade de Ciências, Portugal
 Fundação para a Ciência e a Tecnologia
Concluído
Produções

Publicações

Artigo em revista
  1. Gracinda M. S. Gomes; Ana-Catarina C. Monteiro. "Formations of orthodox semigroups". Semigroup Forum (2023): http://dx.doi.org/10.1007/s00233-023-10390-x.
    10.1007/s00233-023-10390-x
  2. Gracinda M. S. Gomes; Isabel J. Nobre. "Formations of inverse semigroups". Semigroup Forum (2022): http://dx.doi.org/10.1007/s00233-022-10290-6.
    10.1007/s00233-022-10290-6
  3. Bernardo Hipólito Fernandes; Gracinda M.S. Gomes. "¿¿-Algebras". Communications in Algebra (2021): http://dx.doi.org/10.1080/00927872.2021.1910283.
    10.1080/00927872.2021.1910283
  4. Bernardo H. Fernandes; Gracinda M. S. Gomes. "A topological shuttle between inequalities and pseudoinequalities". Semigroup Forum (2021): http://dx.doi.org/10.1007/s00233-021-10167-0.
    10.1007/s00233-021-10167-0
  5. Mário J.J. Branco; Gracinda M.S. Gomes; Jean-Éric Pin; Xaro Soler-Escrivà. "On formations of monoids". Journal of Pure and Applied Algebra (2020): http://dx.doi.org/10.1016/j.jpaa.2020.106401.
    10.1016/j.jpaa.2020.106401
  6. Mário Branco; Gracinda M.S. Gomes; Pedro V. Silva. "On the semigroup rank of a group". Semigroup Forum (2019): http://dx.doi.org/10.1007/s00233-018-9982-x.
    10.1007/s00233-018-9982-x
  7. João Araújo; Wolfram Bentz; Gracinda M. S. Gomes. "Congruences on direct products of transformation and matrix monoids". Semigroup Forum (2018): http://dx.doi.org/10.1007/s00233-018-9931-8.
    10.1007/s00233-018-9931-8
  8. Mário J.J. Branco; Gracinda M.S. Gomes; Victoria Gould; Yanhui Wang. "Ehresmann monoids: Adequacy and expansions". Journal of Algebra (2018): http://dx.doi.org/10.1016/j.jalgebra.2018.06.036.
    10.1016/j.jalgebra.2018.06.036
  9. Branco, M.J.J.; Gomes, G.M.S.; Silva, P.V.. "Takahasi semigroups". Forum Mathematicum 29 5 (2017): 1145-1161. http://www.scopus.com/inward/record.url?eid=2-s2.0-85028881447&partnerID=MN8TOARS.
    10.1515/forum-2015-0059
  10. Branco, M.J.J.; Gomes, G.M.S.; Gould, V.. "Ehresmann monoids". Journal of Algebra 443 (2015): 349-382. http://www.scopus.com/inward/record.url?eid=2-s2.0-84939158722&partnerID=MN8TOARS.
    10.1016/j.jalgebra.2015.06.035
  11. Gomes, G.M.S.; Santa-Clara, C.; Soares, F.. "The semigroup ring of a restriction semigroup with an inverse skeleton". Semigroup Forum 90 2 (2015): 449-474. http://www.scopus.com/inward/record.url?eid=2-s2.0-84939877594&partnerID=MN8TOARS.
    10.1007/s00233-014-9612-1
  12. Gracinda M. S. Gomes; Nik Ruškuc. "John Macintosh Howie: work and legacy". Semigroup Forum (2014): http://dx.doi.org/10.1007/s00233-014-9628-6.
    10.1007/s00233-014-9628-6
  13. Gomes, G.M.S.; Gould, V.. "Left adequate and left Ehresmann monoids II". Journal of Algebra 348 1 (2011): 171-195. http://www.scopus.com/inward/record.url?eid=2-s2.0-80755163588&partnerID=MN8TOARS.
    10.1016/j.jalgebra.2011.09.006
  14. Branco, M.J.J.; Gomes, G.M.S.; Gould, V.. "Left adequate and left Ehresmann monoids". International Journal of Algebra and Computation 21 7 (2011): 1259-1284. http://www.scopus.com/inward/record.url?eid=2-s2.0-82955194542&partnerID=MN8TOARS.
    10.1142/S0218196711006935
  15. Fernandes, V.H.; Gomes, G.M.S.; Jesus, M.M.. "The cardinal and the idempotent number of various monoids of transformations on a finite chain". Bulletin of the Malaysian Mathematical Sciences Society 34 1 (2011): 79-85. http://www.scopus.com/inward/record.url?eid=2-s2.0-79952346644&partnerID=MN8TOARS.
  16. Branco, M.J.J.; Gomes, G.M.S.; Gould, V.. "Extensions and covers for semigroups whose idempotents form a left regular band". Semigroup Forum 81 1 (2010): 51-70. http://www.scopus.com/inward/record.url?eid=2-s2.0-77954860335&partnerID=MN8TOARS.
    10.1007/s00233-010-9239-9
  17. Fountain, J.; Gomes, G.; Gould, V.. "Membership of A ¿ G for classes of finite weakly abundant semigroups". Periodica Mathematica Hungarica 59 1 (2009): 9-36. http://www.scopus.com/inward/record.url?eid=2-s2.0-71449109624&partnerID=MN8TOARS.
    10.1007/s10998-009-9009-1
  18. Fernandes, V.H.; Gomes, G.M.S.; Jesus, M.M.. "Congruences on monoids of transformations preserving the orientation on a finite chain". Journal of Algebra 321 3 (2009): 743-757. http://www.scopus.com/inward/record.url?eid=2-s2.0-57649230089&partnerID=MN8TOARS.
    10.1016/j.jalgebra.2008.11.005
  19. Branco, M.J.J.; Gomes, G.M.S.. "The generalized Szendrei expansion of an R-unipotent semigroup". Acta Mathematica Hungarica 123 1-2 (2009): 11-26. http://www.scopus.com/inward/record.url?eid=2-s2.0-64549087227&partnerID=MN8TOARS.
    10.1007/s10474-009-8025-1
  20. Fountain, J.; Gomes, G.M.S.; Gould, V.. "The free ample monoid". International Journal of Algebra and Computation 19 4 (2009): 527-554. http://www.scopus.com/inward/record.url?eid=2-s2.0-67650787423&partnerID=MN8TOARS.
    10.1142/S0218196709005214
  21. Gomes, G.M.S.; Gould, V.. "Fundamental semigroups having a band of idempotents". Semigroup Forum 77 2 (2008): 279-299. http://www.scopus.com/inward/record.url?eid=2-s2.0-52949146037&partnerID=MN8TOARS.
    10.1007/s00233-007-9041-5
  22. Gomes, G.M.S.; Szendrei, M.B.. "Even covers for left ample semigroups". Semigroup Forum 74 2 (2007): 293-305. http://www.scopus.com/inward/record.url?eid=2-s2.0-34547338444&partnerID=MN8TOARS.
    10.1007/s00233-006-0668-4
  23. Gomes, G.M.S.; Szendrei, M.B.. "Almost factorizable weakly ample semigroups". Communications in Algebra 35 11 (2007): 3503-3523. http://www.scopus.com/inward/record.url?eid=2-s2.0-35448996831&partnerID=MN8TOARS.
    10.1080/00927870701509503
  24. Gomes, G.M.S.. "The generalized prefix expansion of a weakly left ample semigroup". Semigroup Forum 72 3 (2006): 387-403. http://www.scopus.com/inward/record.url?eid=2-s2.0-33744905203&partnerID=MN8TOARS.
    10.1007/s00233-005-0522-0
  25. Fountain, J.; Gomes, G.M.S.. "Proper covers of ample monoids". Proceedings of the Edinburgh Mathematical Society 49 2 (2006): 277-289. http://www.scopus.com/inward/record.url?eid=2-s2.0-33744807444&partnerID=MN8TOARS.
    10.1017/S0013091504000070
  26. Fountain, J.; Gomes, G.M.S.. "Finite abundant semigroups in which the idempotents form a subsemigroup". Journal of Algebra 295 2 (2006): 303-313. http://www.scopus.com/inward/record.url?eid=2-s2.0-31044436904&partnerID=MN8TOARS.
    10.1016/j.jalgebra.2005.10.033
  27. Gomes, G.M.S.; Sezinando, H.; Pin, J.-E.. "Presentations of the schützenberger product of n groups". Communications in Algebra 34 4 (2006): 1213-1235. http://www.scopus.com/inward/record.url?eid=2-s2.0-33645780152&partnerID=MN8TOARS.
    10.1080/00927870500454075
  28. Gomes, G.M.S.. "Proper extensions of weakly left ample semigroups". Acta Mathematica Hungarica 109 1-2 (2005): 33-51. http://www.scopus.com/inward/record.url?eid=2-s2.0-27844527526&partnerID=MN8TOARS.
    10.1007/s10474-005-0233-8
  29. Fernandes, V.H.; Gomes, G.M.S.; Jesus, M.M.. "Presentations for some monoids of partial transformations on a finite chain". Communications in Algebra 33 2 (2005): 587-604. http://www.scopus.com/inward/record.url?eid=2-s2.0-23944439698&partnerID=MN8TOARS.
    10.1081/AGB-200047446
  30. Fernandes, V.H.; Gomes, G.M.S.; Jesus, M.M.. "Congruences on monoids of order-preserving or order-reversing transformations on a finite chain". Glasgow Mathematical Journal 47 2 (2005): 413-424. http://www.scopus.com/inward/record.url?eid=2-s2.0-23944469071&partnerID=MN8TOARS.
    10.1017/S0017089505002648
  31. Fernandes, Vítor; Gomes, Gracinda; Jesus, Manuel. "Presentations for Some Monoids of Injective Partial Transformations on a Finite Chain". Southeast Asian Bulletin of Mathematics 28 (2004): 903-918.
  32. Auinger, K.; Gomes, G.M.S.; Gould, V.; Steinberg, B.. "An application of a theorem of Ash to finite covers". Studia Logica 78 1-2 (2004): 45-57. http://www.scopus.com/inward/record.url?eid=2-s2.0-35948958664&partnerID=MN8TOARS.
  33. Gomes, G.M.S.; Gould, V.. "Finite Proper Covers in a Class of Finite Semigroups with Commuting Idempotents". Semigroup Forum 66 3 (2003): 433-454. http://www.scopus.com/inward/record.url?eid=2-s2.0-1642277929&partnerID=MN8TOARS.
  34. Gomes, G.M.S.; Gould, V.. "Fundamental Ehresmann Semigroups". Semigroup Forum 63 1 (2001): 11-33. http://www.scopus.com/inward/record.url?eid=2-s2.0-0042911865&partnerID=MN8TOARS.
  35. Araújo, I.M.; Branco, M.J.J.; Fernandes, V.H.; Gomes, G.M.S.; Ruškuc, N.. "On Generators and Relations for Unions of Semigroups". Semigroup Forum 63 1 (2001): 49-62. http://www.scopus.com/inward/record.url?eid=2-s2.0-0003112080&partnerID=MN8TOARS.
    10.1007/s002330010053
  36. Gomes, G.M.S.; Giraldes, E.; McAlister, D.B.. "On a Class of Lattice Ordered Inverse Semigroups". Journal of Algebra 230 2 (2000): 496-517. http://www.scopus.com/inward/record.url?eid=2-s2.0-0034662532&partnerID=MN8TOARS.
    10.1006/jabr.2000.8324
  37. "Graph expansions of unipotent monoids". (2000): http://www.tandfonline.com/doi/abs/10.1080/00927870008841083#preview.
    10.1080/00927870008841083
  38. Fountain, J.; Gomes, G.M.S.. "Primitive inverse congruences on categorical semigroups". Proceedings of the Edinburgh Mathematical Society 43 2 (2000): 395-413. http://www.scopus.com/inward/record.url?eid=2-s2.0-23044517926&partnerID=MN8TOARS.
    10.1017/S001309150002099X
  39. Gomes, G.M.S.; Gould, V.. "Proper weakly left ample semigroups". International Journal of Algebra and Computation 9 6 (1999): 721-739. http://www.scopus.com/inward/record.url?eid=2-s2.0-0347024563&partnerID=MN8TOARS.
    10.1142/S0218196799000412
  40. Fountain, J.; Gomes, G.M.S.; Gould, V.. "A Munn type representation for a class of E-semiadequate semigroups". Journal of Algebra 218 2 (1999): 693-714. http://www.scopus.com/inward/record.url?eid=2-s2.0-0033566520&partnerID=MN8TOARS.
    10.1006/jabr.1999.7871
  41. "Enlargements, semiabundancy and unipotent monoids". (1999): http://www.tandfonline.com/doi/abs/10.1080/00927879908826450#preview.
    10.1080/00927879908826450
  42. Gomes, G.M.S.; Szendrei, M.B.. "Idempotent pure extensions by inverse semigroups via quivers". Journal of Pure and Applied Algebra 127 1 (1998): 15-38. http://www.scopus.com/inward/record.url?eid=2-s2.0-0032063244&partnerID=MN8TOARS.
    10.1016/S0022-4049(97)00110-2
  43. Gomes, G.M.S.; Howie, J.M.. "Semigroups with zero whose idempotents form a subsemigroup". Royal Society of Edinburgh - Proceedings A 128 2 (1998): 265-281. http://www.scopus.com/inward/record.url?eid=2-s2.0-22044454302&partnerID=MN8TOARS.
  44. "A P-theorem for inverse semigroups with zero". Portugal. Math. (1996):
  45. Gomes, G.M.S.. "Idempotent Endomorphisms of an Independence Algebra of Finite Rank". Proceedings of the Edinburgh Mathematical Society 38 1 (1995): 107-116. http://www.scopus.com/inward/record.url?eid=2-s2.0-84973981377&partnerID=MN8TOARS.
    10.1017/S0013091500006234
  46. "Proper left type-A covers". Portugal. Math., (1994):
  47. John Fountain; Gracinda M. S. Gomes. "Proper left type-A monoids revisited". Glasgow Mathematical Journal (1993): http://dx.doi.org/10.1017/s0017089500009873.
    10.1017/s0017089500009873
  48. Gomes, G.M.S.. "A characterization of the group congruences on a semigroup". Semigroup Forum 46 1 (1993): 48-53. http://www.scopus.com/inward/record.url?eid=2-s2.0-51249162950&partnerID=MN8TOARS.
    10.1007/BF02573543
  49. Fountain, J.; Gomes, G.M.S.. "Left proper E-dense monoids". Journal of Pure and Applied Algebra 80 1 (1992): 1-27. http://www.scopus.com/inward/record.url?eid=2-s2.0-38249012155&partnerID=MN8TOARS.
    10.1016/0022-4049(92)90066-O
  50. Gomes, G.M.S.; Howie, J.M.. "On the ranks of certain semigroups of order-preserving transformations". Semigroup Forum 45 1 (1992): 272-282. http://www.scopus.com/inward/record.url?eid=2-s2.0-0000063566&partnerID=MN8TOARS.
    10.1007/BF03025769
  51. "Group congruences on eventually inverse semigroup". Portugal. Math. (1992):
  52. John Fountain; Gracinda M. S. Gomes. "The Szendrei expansion of a semigroup". Mathematika (1990): http://dx.doi.org/10.1112/s0025579300012973.
    10.1112/s0025579300012973
  53. Gomes, G.M.S.. "Orthodox congruences on regular semigroups". Semigroup Forum 37 1 (1988): 149-166. http://www.scopus.com/inward/record.url?eid=2-s2.0-51249170819&partnerID=MN8TOARS.
    10.1007/BF02573131
  54. Gomes, G.M.S.; Howie, J.M.. "Nilpotents in finite symmetric inverse semigroups". Proceedings of the Edinburgh Mathematical Society 30 3 (1987): 383-395. http://www.scopus.com/inward/record.url?eid=2-s2.0-84976003287&partnerID=MN8TOARS.
    10.1017/S0013091500026778
  55. "ON THE RANKS OF CERTAIN FINITE-SEMIGROUPS OF TRANSFORMATIONS". (1987):
    10.1017/S0305004100066780
  56. Gomes, G.M.S.. "The lattice of r-unipotent congruences on a regular semigroup". Semigroup Forum 33 1 (1986): 159-173. http://www.scopus.com/inward/record.url?eid=2-s2.0-51649155385&partnerID=MN8TOARS.
    10.1007/BF02573190
  57. Gomes, M.S.. "Some results on congruences on r-unipotent semigroups". Semigroup Forum 33 1 (1986): 175-185. http://www.scopus.com/inward/record.url?eid=2-s2.0-51649148673&partnerID=MN8TOARS.
    10.1007/BF02573191
  58. Gomes, G.M.S.. "R-unipotent congruences on regular semigroups". Semigroup Forum 31 1 (1985): 265-280. http://www.scopus.com/inward/record.url?eid=2-s2.0-51249171525&partnerID=MN8TOARS.
    10.1007/BF02572656
  59. Gomes, G.M.S.. "On Left Quasinormal Orthodox Semigroups". Proceedings of the Royal Society of Edinburgh: Section A Mathematics 95 1-2 (1983): 59-71. http://www.scopus.com/inward/record.url?eid=2-s2.0-64549097157&partnerID=MN8TOARS.
    10.1017/S0308210500015791
  60. T. S. Blyth; Gracinda M. S. Gomes. "On the compatibility of the natural order on a regular semigroup". Proceedings of the Royal Society of Edinburgh: Section A Mathematics (1983): http://dx.doi.org/10.1017/s0308210500016140.
    10.1017/s0308210500016140
Livro
  1. Gracinda M.S. Gomes. Anéis e Corpos - uma introdução (2021). Portugal. 2021.
  2. Gomes, Gracinda Maria dos Santos. Aspects of order and congruence relations on regular semigroups. 1983.
Distinções

Título

2022 Sócia Honorária