Jorge Vitória
Senior Lecturer/Professore Associato in Mathematics
Click here for institutional webpage (unipd)
(previous institutional webpage (unica))
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email: jorge "dot" vitoria "at" unipd "dot" it
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address: Dip. Matematica "Tullio Levi-Civita"
Università degli Studi di Padova
Torre Archimede, Via Trieste, 63
35121, Padova, Italy
Short CV
Personal
Born in Porto, Portugal, 1984
Education
2006 - 2010 PhD in Mathematics at University of Warwick
2002 - 2006 Licenciatura in Mathematics at Faculdade de Ciências, Universidade do Porto
Employment
2022 - present, Senior Lecturer (Professore Associato) at Università degli Studi di Padova
2021 - 2022, Senior Lecturer (Professore Associato) at Università degli Studi di Cagliari
2018 - 2021, Lecturer (RTDb) at Università degli Studi di Cagliari
2016 - 2018, Postdoctoral researcher, City, University of London
2015 - 2016, Postdoctoral researcher (AdR), Università degli Studi di Verona
2013 - 2015, Marie Curie Fellow, Università degli Studi di Verona
2013, Postdoctoral researcher, BIREP, Universität Bielefeld
2010 - 2013, Postdoctoral researcher, Institut für Algebra und Zahlentheorie, University of Stuttgart
A full CV is available here.
Research Interests
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
Publications and Preprints
Submitted preprints
Submitted preprints
joint with Lidia Angeleri Hügel and David Pauksztello, Fishing for complements. (arxiv)
Mutations and derived equivalences for commutative noetherian rings, To appear in the Proceedings of ICRA 2022 (arXiv)
joint with Lidia Angeleri Hügel, Rosanna Laking and Jan Stovicek, Mutations and torsion pairs. (arXiv)
Journal Articles
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.
Conference Proceedings
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).
Outreach
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).
Notes, slides and other texts
Slides of the lecture series Cosilting mutation: what, when, where? (2023), at the Online Workship "Mutations in Representation Theory of Algebras" organised by the IPM - Isfahan.
Slides of the talk Ring epimorphisms and localisations in representation theory, at the conference "Matemáticos portugueses pelo mundo" at the University of Porto (see also the survey Representations of commutative rings via the prime spectrum).
Exercises and solutions in Silting Theory, for the LMS-CMI Research School New Trends in Representation Theory: The Impact of Cluster Theory (Leicester, UK, June 2017)
Slides of a talk to (prospective) PhD students in Padova and Verona: A visual introduction to Tilting and a companion exposition text available in this collection (pp. 147-155)
Lecture notes of a mini-course for Master and PhD students, Verona (2012): Localisations in Algebra and Geometry
Slides from Schwerpunkttage Thurnau 2012: t-structures, recollements and silting objects
Notes from a talk at ICRA 2012 in Bielefeld: Glueing silting or how two hearts become one
Equivalences for noncommutative projective spaces, unpublished preprint (2010) (arXiv)
Participation in research projects
Ongoing
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.
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.
Network on Silting Theory, (Deutsche Forschungsgemeineschaft), Member of the Steering Commitee, Principal Investigators: Frederik Marks and Alexandra Zvonareva
Past
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: Jorge Vitória
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: Jorge Vitória.
Teaching and supervision
Thesis supervision
Thesis supervision
PhD students:
Anastasios Slaftsos (since October 2023)
Enrico Sabatini (since November 2022)
MSc students:
August 2023: Francesco Angeli, Strong global dimension and piecewise hereditary algebras.
September 2022: Daria Dessì, Topics for persistence homology: quivers and spreads.
September 2022: Enrico Sabatini, On finiteness properties of local cohomology modules.
July 2022: Michele Gaviano, Rings of fractions, universal localisations and ring epimorphisms.
February 2022: Manuel Pusceddu, Torsion pairs and derived equivalences for path algebras of type A.
Undegraduate projects/thesis
September 2021: Marco Ferrara, final undergraduate project (in italian), Polinomi ciclotomici e applicazioni.
Courses
At the University of Padova:
2021/2022 and 2022/2023: Rings and Modules
2021/2022 and 2022/2023: Matematica (for Chemistry, Industrial Chemistry and Material Sciences students, in italian)
At the University of Cagliari:
2019 - 2022: Introduzione alla teoria delle categorie (Reading course, in italian)
2019 - 2022: Introduzione alla teoria delle rappresentazioni (Reading course, in italian)
2020/2021: Algebra 2, Algebra Superiore (in italian)
2019/2020: Matematica Discreta (for Computer Sciences students, in italian), Logica Matematica (in italian)
2018/2019: Matematica 2 (for Chemistry students, in italian)
At City, University of London:
2017/2018: Mathematics for economists - Post A level (2)
2016/2017: Topology
At the University of Verona:
2015/2016: Algebra lineare con elementi di geometria (in italian)
Seminar topics for MSc students (4 CFU)
Events
Co-organisation of meetings/conferences
Silting Theory, Algebras and Representations, 12-16 September, 2022, Charles University Prague.
Online Satellite event, Homological methods in representation theory - a conference in honour of Lidia Angeleri Hügel, February 22 - 23, 2022.
Homological methods in representation theory - a conference in honour of Lidia Angeleri Hügel, October 3 - 8, 2021, Fraueninsel (Chiemsee), Abtei Frauenwörth, Germany.
Algebra day in Sardinia, Cagliari, May 2020 (CANCELLED)
Seventy-sixth BLOC meeting, London, March 2017
Triangulated categories in representation theory, geometry and topology, Stuttgart, March 2016
Silting theory and related topics, Verona, July 2015
Annual conference of the DFG priority programme in representation theory, SPP 1388, Bad Boll, March 2013 (local organiser)
Workshop on t-structures and related topics, Stuttgart 2011
Other events
FD Seminar: Online seminar on representation theory of finite-dimensional algebras
Colloquia Patavina (Padova)
London Algebra Colloquium (Birkbeck/City/Imperial College/Queen Mary)
MALGA seminar (Verona/Padova)
BIREP seminar (Bielefeld)
IAZ Oberseminar (Stuttgart)
Links
Institutions
Dipartimento di Matematica "Tullio Levi-Civita", Università degli Studi di Padova
Dipartimento di Matematica e Informatica, Università degli Studi di Cagliari
BIREP: Representations of finite dimensional algebras at Bielefeld
CMUP: Centre for Mathematics of the University of Porto
Tools
FDList: Information list for representation theory of finite dimensional algebras