Marco Arien Mackaaij
Professor associado
Faculdade de Ciências e Tecnologia
Subsistema
Docentes Universitário
Regime
Exclusividade
Vínculo
CT em Funções Públicas por tempo indeterminado
MARCO MACKAAIJ. PhD in Mathematics, Instituto Superior Técnico, Lisbon, Portugal, 1999/12/21. Associate Professor in Mathematics at the Universidade do Algarve. Research: categorified quantum algebras, 2-representation theory and link homology.
Atividades
Atividades
2023/01/25. Apresentação oral de trabalho. 2-Representations of affine type A Soergel bimodules: some examples and observations.. TQFT-club seminar. Instituto Superior Técnico (Lisboa).
2023/06/23. Júri de grau académico. On Rasmussen's s-invariant and the search for exotic definite 4-manifolds. . Arguente. João Miguel Rebelo de Oliveira (Mestrado). Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento.
2022/07/20. Júri de grau académico. Hecke Algebras and Topological Quantum Field Theories. Arguente principal. Bernardo Mariz Ferreira Leite da Cunha (Mestrado). Universidade do Porto.
2022/07/20. Apresentação oral de trabalho. 2-Representations of affine type A Soergel bimodules: some examples and observations.. Algebra and Geometry Seminar. Universidade do Porto (Porto).
2022/07/11 - 2022/07/15. Curso / Disciplina lecionado. Categorification. Research School on Bicategories, Categorification and Quantum Theory (Doctor of Philosophy). London Mathematical Society; University of Leeds.
2022/05/03. Apresentação oral de trabalho. 2-Representations of affine type A Soergel bimodules: some examples and observations.. Uppsala Algebra Seminar. University of Uppsala (Uppsala, Suécia).
2022/03/14. Apresentação oral de trabalho. 2-Representations of affine type A Soergel bimodules: some examples and observations. . Pure Mathematics Seminar. University of East Anglia (Norwich, Reino Unido).
2019/01/24. Apresentação oral de trabalho. The 2-theory of Soergel bimodules of finite Coxeter type: a road map to the complete classification of all simple transitive 2-representations.. Geometry and Topology Seminar. Universidade do Porto (Porto, Portugal).
2019/01/23. Apresentação oral de trabalho. The 2-representation theory of Soergel bimodules. Seminário de Álgebra. Universidade de Coimbra (Coimbra, Portugal).
2019/01/10. Apresentação oral de trabalho. The 2-theory of Soergel bimodules of finite Coxeter type: a road map to the complete classification of all simple transitive 2-representations.. Topological Quantum Field Theory Seminar. Instituto Superior Técnico (Lisboa, Portugal).
2019/07/17. Júri de grau académico. Representations on diagrams of categories and applications to parabolic bundles. Arguente principal. Rui Rodrigues de Abreu Fernandes Prezado (Mestrado). Universidade do Porto.
2019/07/12. Apresentação oral de trabalho. The 2-representation theory of Soergel bimodules of finite Coxeter type. Representations of monoidal categories and 2-categories. University of East Anglia (Norwich, Reino Unido).
2019/07/11. Apresentação oral de trabalho. Finitary 2-representations and (co)algebra 1-morphisms. Representations of monoidal categories and 2-categories. University of East Anglia (Norwich, Reino Unido).
2019/06/17. Apresentação oral de trabalho. The 2-representation theory of Soergel bimodules. . Mathematical Physics Seminar. University of Zurich (Zurique, Suiça).
2019/04/23. Apresentação oral de trabalho. The 2-representation theory of Soergel bimodules. . Algebra and Geometry Seminar. Uppsala University (Uppsala, Suécia).
2017/10/28. Júri de grau académico. Pseudomonads and Descent. Arguente. Fernando Lucatelli Nunes (Doutoramento). Universidade de Coimbra.
2016/01/19. Júri de grau académico. Simple transitive 2-representations of Soergel bimodules in type B2 (tese de "Licentiate"). Arguente principal. Jacob Zimmermann (Outro). Uppsala Universitet.
2016/09/30. Júri de grau académico. The quotient module, coring depth and factorisation algebra. Arguente principal. Alberto Hernandez Alvarez (Doutoramento). Universidade do Porto.
2014/09/19. Júri de grau académico. The Depth Theory of a Hopf algebra in its Smash Product. Arguente principal. Christopher J. Young (Doutoramento). Universidade do Porto.
2013/07/10. Júri de grau académico. Sur l'homologies sl(3) des enchevêtrements; algèbres de Khovanov-Kuperberg. Arguente principal. Louis-Hadrien Robert (Doutoramento). Université Paris Diderot.
2013/07/02. Júri de grau académico. Categorification and applications in topology and
representation theory. Vogal. Daniel Tubbenhauer (Doutoramento). Georg-August-Universität Göttingen.
representation theory. Vogal. Daniel Tubbenhauer (Doutoramento). Georg-August-Universität Göttingen.
2013/03/22. Júri de grau académico. Mapping spaces of Gray-categories. Arguente principal. Björn Gohla (Doutoramento). Universidade do Porto.
2010/07/29. Júri de grau académico. Odd Khovanov homology for virtual knots. Vogal. Diana Manuel Fernandes Tavares (Mestrado). Universidade de Lisboa Instituto Superior Técnico.
2009/12/23. Júri de grau académico. Geometric quantization and degenerations of complex structures for two families of compact
manifolds. Vogal. Thomas Baier (Doutoramento). Universidade de Lisboa Instituto Superior Técnico.
manifolds. Vogal. Thomas Baier (Doutoramento). Universidade de Lisboa Instituto Superior Técnico.
2008/07/08. Júri de grau académico. A categorification of the quantum sl(N)-link polynomials using foams. Orientador. Pedro Vaz (Doutoramento). Universidade do Algarve - Campus de Gambelas.
2006/03/31. Júri de grau académico. Khovanov homology of links and graphs. Arguente. Marko Stosic (Doutoramento). Universidade de Lisboa Instituto Superior Técnico.
2003/11/28. Júri de grau académico. Homotopy Quantum Field Theories. Arguente. Gonçalo Violante Rodrigues (Doutoramento). Universidade de Lisboa Instituto Superior Técnico.
Projetos
Projetos
2018/07 - 2021/06. Higher Structures and Applications.
2013/05 - 2016/04. Geometry and Mathematical-Physics.
2010/01 - 2013/06. New Geometry and Topology.
2007/01 - 2009/12. Quantum Topology.
2005/06 - 2008/06. Quantum Topology.
2007/03 - 2008/02. Symmetries, gravity and strings.
Produções
Marco Mackaay; Volodymyr Mazorchuk; Vanessa Miemietz; Xiaoting Zhang. 2018. "ANALOGUES OF CENTRALIZER SUBALGEBRAS FOR FIAT -CATEGORIES AND THEIR -REPRESENTATIONS". Journal of the Institute of Mathematics of Jussieu. https://doi.org/10.1017/S1474748018000555
Marco Mackaay; Alistair Savage. 2018. "Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification". Journal of Algebra, 505: 150-193. https://doi.org/10.1016/j.jalgebra.2018.03.004
Mackaay, M.; Mazorchuk, V.. 2017. "Simple transitive 2-representations for some 2-subcategories of Soergel bimodules". Journal of Pure and Applied Algebra, 221 (3): 565-587. https://doi.org/10.1016/j.jpaa.2016.07.006
Mackaay, M.; Thiel, A.-L.. 2017. "Categorifications of the extended affine Hecke algebra and the affine q-Schur algebra S(n, r) for 3 = r < n". Quantum Topology, 8 (1): 113-203. https://doi.org/10.4171/QT/88
MACKAAIJ, MARCO. 2015. "A diagrammatic categorification of the affine q-schur algebra s (n; n) for n = 3". Pacific Journal of Mathematics 278 (1) ,pp.201-233. https://doi.org/10.2140/pjm.2015.278.201
MACKAAIJ, MARCO. 2015. "A diagrammatic categorification of the q-schur algebra". Quantum Topology Volume 4, Issue 1, 2015, Pages 1-75. https://doi.org/10.4171/QT/34
Mackaay, M.; Pan, W.; Tubbenhauer, D.. 2014. "The Sl3-web algebra". Mathematische Zeitschrift, 277 (1-2): 401-479. https://doi.org/10.1007/s00209-013-1262-6
Mackaay, M.. 2014. "The slN-web algebras and dual canonical bases". Journal of Algebra, 409: 54-100. https://doi.org/10.1016/j.jalgebra.2014.02.036
MACKAAIJ, MARCO. 2013. "Erratum: A remark on Rasmussen’s invariant of knots". J. Knot and its Ramifications 22(1) (2013), 1392001, 1 p. https://doi.org/10.1142/S0218216513920016
Khovanov, M.; Lauda, A.D.; Mackaay, M.; Stosíc, M.. 2012. "Extended graphical calculus for categorified quantum sl(2)". Memoirs of the American Mathematical Society, 219 (1029): 1-87. https://doi.org/10.1090/S0065-9266-2012-00665-4
Mackaay, M.; Stošic, M.; Vaz, P.. 2011. "The 1,2-coloured homfly-pt link homology". Transactions of the American Mathematical Society, 363 (4): 2091-2124. https://doi.org/10.1090/S0002-9947-2010-05155-4
MACKAAIJ, MARCO. 2010. "The diagrammatic Soergel category and sl(N)-foams". Int. J. Math. and Math. Sci., vol. 2010, Article ID 468968, 2010. https://doi.org/10.1155/2010/468968
Mackaay, M.; Stošic, M.; Vaz, P.. 2009. "Sl(N)-link homology (N= 4) using foams and the Kapustin-Li formula". Geometry and Topology, 13 (2): 1075-1128. https://doi.org/10.2140/gt.2009.13.1075
Mackaay, M.; Vaz, P.. 2008. "The foam and the matrix factorization sl3 link homologies are equivalent". Algebraic and Geometric Topology, 8 (1): 309-342. https://doi.org/10.2140/agt.2008.8.309
Mackaay, M.; Vaz, P.. 2007. "The universal sl3-link homology". Algebraic and Geometric Topology, 7 (1): 1135-1169. https://doi.org/10.2140/agt.2007.7.1135
Mackaay, M.; Turner, P.; Vaz, P.. 2007. "A remark on Rasmussen's invariant of knots". Journal of Knot Theory and its Ramifications, 16 (3): 333-344. https://doi.org/10.1142/S0218216507005312
Mackaay, M.; Turner, P.. 2007. "Bar-Natan's Khovanov homology for coloured links". Pacific Journal of Mathematics, 229 (2): 429-446. https://doi.org/10.2140/pjm.2007.229.429
Barrett, J.W.; Mackaay, M.. 2006. "Categorical representations of categorical groups". Theory and Applications of Categories, 16 (10): 529-557. http://www.scopus.com/inward/record.url?eid=2-s2.0-33748333184&partnerID=MN8TOARS
MACKAAIJ, MARCO. 2003. "A note on the holonomy in twisted bundles". Cah. Topol. G´eom. Diff´er. Cat´eg. 44 (2003), no. 1, 39-62.. https://eudml.org/doc/91665
Mackaay, M.; Picken, R.. 2002. "Holonomy and parallel transport for Abelian gerbes". Advances in Mathematics, 170 (2): 287-339. https://doi.org/10.1016/S0001-8708(02)92085-2
Mackaay, M.. 2000. "Finite groups, spherical 2-categories, and 4-manifold invariants". Advances in Mathematics, 153 (2): 353-390. https://doi.org/10.1006/aima.1999.1909
Mackaay, M.. 1999. "Spherical 2-categories and 4-manifold invariants". Advances in Mathematics, 143 (2): 288-348. https://doi.org/10.1006/aima.1998.1798
Mackaay, M.; Webster, B.. 2018. "Categorified skew Howe duality and comparison of knot homologies". Advances in Mathematics, 330: 876-945. https://doi.org/10.1016/j.aim.2018.03.034
Kildetoft, T.; Mackaay, M.; Mazorchuk, V.; Zimmermann, J.. 2019. "Simple transitive 2-representations of small quotients of soergel bimodules". Transactions of the American Mathematical Society, 371 (8): 5551-5590. https://doi.org/10.1090/tran/7456
Mackaay, M.; Yonezawa, Y.. 2019. "sl<inf>N</inf>-web categories and categorified skew Howe duality". Journal of Pure and Applied Algebra, 223 (5): 2173-2229. https://doi.org/10.1016/j.jpaa.2018.07.013
Mackaay, M.; Mazorchuk, V.; Miemietz, V.; Tubbenhauer, D.. 2019. "Simple transitive 2-representations via (co-)algebra 1-morphisms". Indiana University Mathematics Journal, 68 (1): 1-33. https://doi.org/10.1512/iumj.2019.68.7554
MacKaay, M.; Mazorchuk, V.; Miemietz, V.; Tubbenhauer, D.. 2020. "Trihedral soergel bimodules". Fundamenta Mathematicae, 248 (3): 219-300. https://doi.org/10.4064/fm566-3-2019
MACKAAIJ, MARCO; Tubbenhauer, D.. 2019. "Two-color Soergel Calculus and Simple Transitive 2-representations". Canadian Journal of Mathematics, 71 (6): 1523-1566. https://doi.org/10.4153/cjm-2017-061-2
2021. "Finitary birepresentations of finitary bicategories". Forum Mathematicum, 33 (5): 1261-1320. https://doi.org/10.1515/forum-2021-0021
Mackaay, M.; Mazorchuk, V.; Miemietz, V.; Tubbenhauer, D.; Zhang, X.. 2023. "Simple transitive 2-representations of Soergel bimodules for finite Coxeter types". Proceedings of the London Mathematical Society. https://doi.org/10.1112/plms.12515
Marco Mackaay; Vanessa Miemietz; Pedro Vaz. 2024. "Evaluation birepresentations of affine type A Soergel bimodules". Advances in Mathematics. https://doi.org/10.1016/j.aim.2023.109401
