Jorge Vitória
Senior Lecturer/Professore Associato in Mathematics
RESEARCH
RESEARCH
Derived categories in representation theory; Torsion pairs in abelian and triangulated categories, in particular t-structures and co-t-structures; Compactly generated triangulated categories and their definable subcategories; Localisations of rings and categories; Tilting/Silting theory; Finite-dimensional algebras, commutative noetherian rings and noetherian algebras.
joint with Michal Hrbek and Sergio Pavon, Mutation and the Gabriel spectrum. (arXiv)
joint with Lidia Angeleri Hügel and David Pauksztello, Fishing for complements, Nagoya Math J. Published online (2025), 1-26. doi:10.1017/nmj.2025.10070. (arxiv)
joint with Lidia Angeleri Hügel, Rosanna Laking and Jan Stovicek, Mutations and torsion pairs, Alg. Number Th. 19, no.7 (2025), 1313--1368. (arXiv)
joint with Sergio Pavon, Hearts for commutative noetherian rings: torsion pairs and derived equivalences, Doc. Math. 26 (2021), 829--871. (arXiv)
joint with Lidia Angeleri Hügel, Frederik Marks, Jan Stovicek and Ryo Takahashi, Flat ring epimorphisms and universal localisations of commutative rings, Q. J. Math. 71(4) (2020), 1489–1520. (arXiv)
joint with Rosanna Laking, Definability and approximations in triangulated categories, Pacific J. Math., 306-2 (2020), 557--586. (arXiv)
joint with Lidia Angeleri Hügel and Frederik Marks, Partial silting objects and smashing subcategories, Math. Z. 296 (2020), 887–900. (arXiv)
joint with Carlos E. Parra, Properties of abelian categories via recollements, J. Pure and Appl. Algebra 223 (2019), 3941--3963. (arXiv)
joint with Frederik Marks, Silting and cosilting classes in derived categories, J. Algebra 501 (2018), 526--544. (arXiv)
joint with Chrysostomos Psaroudakis, Realisation functors in tilting theory, Math. Z. 288(3) (2018), 965--1028. (arXiv)
joint with Lidia Angeleri Hügel and Frederik Marks, Torsion pairs in silting theory, Pacific J. Math. 291-2 (2017), 257--278. (arXiv)
joint with Lidia Angeleri Hügel and Frederik Marks, Silting modules and ring epimorphisms, Adv. Math. 303 (2016) 1044–1076. (arXiv)
joint with Lidia Angeleri Hügel and Frederik Marks, Silting modules, Int. Math. Res. Not. IMRN 2016, no. 4 (2016) 1251--1284. (arXiv)
joint with Frederik Marks, From ring epimorphisms to universal localisations, Forum Math. 27, no.2 (2015), 1139--1161. (arXiv)
joint with Qunhua Liu and Dong Yang, Glueing Silting objects, Nagoya Math. J. 216 (2014), 117--151. (arXiv)
Perverse coherent t-structures through torsion theories, Algebr. Represent. Th. 17, no. 4 (2014), 1181--1206. (arXiv)
joint with Chrysostomos Psaroudakis, Recollements of Module Categories, Appl. Categ. Structures 22, no.4 (2014), 579--593. (arXiv)
joint with Qunhua Liu, t-structures via recollements for piecewise hereditary algebras , J. Pure and Appl. Algebra 216 (2012), no. 4, 837--849. (arXiv)
Mutations Vs. Seiberg duality, Journal of Algebra 321 (2009), no. 3, 816--828 - (arXiv). Here is a Corrigendum to this paper. See also this Chapter of my thesis.
Mutations and derived equivalences for commutative noetherian rings, to appear in Representations of Algebras and Related Topics – Proceedings of the Workshop and the 20th International Conference on Representations of Algebras, ICRA2022 Montevideo (Uruguay) and Buenos Aires (Argentina), 3-12 August 2022, EMS Press (2025). (arXiv)
joint with Lidia Angeleri Hügel and Frederik Marks, A characterisation of τ-tilting finite algebras, in Model Theory of Modules, Algebras and Categories, Contemp. Math. 730, Amer. Math. Soc., Providence, RI (2019) 75--89. (arXiv)
Quantity vs. size in representation theory, Boletim SPM 77 (2019), 151--166 (arXiv).
Representations of commutative rings via the prime spectrum, CIM Bulletin 41 (2019).
Aljavas, Caminhos e representações, (in portuguese) in Números, cirurgias e nós de gravatas, eds: João Pedro Boavida, Rui Pedro Carpentier, Luís Cruz-Filipe, Pedro S. Gonçalves, Eloísa Grifo, David Henriques, Ana Rita Pires, IST Press, Lisbon (2012).
Structures for quivers, algebras and representations, PRIN - Progetto di Rilevante Interesse Nazionale, Associate Investigator for the Research Unit at the University of Padova, Principal Investigator: Lidia Angeleri Hügel.
Network on Silting Theory, (Deutsche Forschungsgemeineschaft), Member of the Steering Commitee, Principal Investigators: Frederik Marks and Alexandra Zvonareva
2022-2024 "Representations of quivers with commutative coefficients", Progetto SID - BIRD Budget Integrato per la Ricerca Dipartimentale 2022, Dipartimento di Matematica "Tullio Levi-Civita", Università degli Studi di Padova, Principal Investigator.
2020-2022 "REDCOM - Reducing complexity in algebra, logic, combinatorics", (Fondazione Cariverona), Principal Investigator: Lidia Angeleri Hügel
2021-2022, "GoAct - The geometry of actions", (Fondazione di Sardegna), Principal Investigator.
2016-2018, "Derived localisations in algebra and homotopy theory" (EPSRC - UK), Principal Investigator: Joseph Chuang
2015-2016, "Categorical localisations: methods and foundations", (Università degli Studi di Verona), Principal Investigator: Lidia Angeleri Hügel
2013-2015, "Tilting theory in derived module categories" (Marie Curie Intra-European Fellowship), Principal Investigator.