Research interests

  • Representation theory of finite-dimensional algebras
  • Purity in compactly generated triangulated and finitely accessible additive categories
  • Large silting and cosilting theory
  • Model theory of modules
Workshop: Purity, Approximation Theory and Spectra (PATHS)
The algebra group at the University of Verona will hold a workshop on the topics of purity, approximation theory and spectra. The workshop will be held at the Grand Hotel San Michele, Cetraro in Calabria, Italy.
Due to the Coronavirus pandemic, the PATHS workshop has been postponed. New dates for the workshop will be announced as soon as possible.

Online seminar: FD Seminar
I am one of the organisers of the FD seminar, a weekly online seminar on the representation theory of finite-dimensional algebras.


  • Classification of cosilting modules in type Ã
    K. Baur and R. Laking
    (Preprint, 2019).
  • Cotilting sheaves over weighted noncommutative regular projective curves
    D. Kussin and R. Laking
    (Preprint, 2019).


  • Definability and approximations in triangulated categories
    R. Laking and J. Vitória
    Pacific Journal of Mathematics, Volume 306, 557-586 (2020).
    Journal · arXiv
  • Purity in compactly generated derivators and t-structures with Grothendieck hearts
    R. Laking
    Mathematische Zeitschrift, Volume 295, 1615-1641 (2020).
    Journal · arXiv
  • Krull-Gabriel dimension and the Ziegler spectrum
    R. Laking
    in Proceedings of the 17th Workshop and International Conference on Representations of Algebras
    Contemporary Mathematics, Volume 705, 115-130 (2018).
  • Krull-Gabriel dimension of domestic string algebras
    R. Laking, M. Prest and G. Puninski
    Transactions of the Amererican Mathematical Society, Volume 370, 4813-4840 (2018).
    Journal · arXiv
  • The Ziegler spectrum for derived-discrete algebras
    K. Arnesen, R. Laking, D. Pauksztello and M. Prest
    Advances in Mathematics, Volume 319, 653-698 (2017).
    Journal · arXiv
  • Morphisms between indecomposable objects in the bounded derived category of a gentle algebra
    K. Arnesen, R. Laking and D. Pauksztello
    Journal of Algebra, Volume 467, 1-366 (2016).
    Journal · arXiv

Curriculum Vitae

Dates Place Position
Current Università degli Studi di Verona, Italy Marie Skłodowska-Curie fellow
Oct 2017 - Sept 2018 MPIM, Bonn, Germany Postdoctoral researcher
Oct 2016 - Sept 2017 Universität Bonn, Germany Postdoctoral researcher
Jun 2016 - Aug 2016 University of Manchester, UK Postdoctoral researcher
Sept 2012 - May 2016 University of Manchester, UK PhD student (Advisor: Mike Prest,
Title: String Algebras in Representation Theory )

Functorial methods in silting theory

Between January 2019 and December 2020 I will be working on a project funded by the Marie Skłodowska-Curie Individual Fellowships program. The project, called Functorial Techniques in Silting Theory, aims to apply methods originating in the model theory of modules to the theory of silting.

A remarkable feature of the model theory of modules is that many model theoretic results can be translated into statements about a certain categories of additive functors and vice versa. This connection with functor categories has given rise to a wide range of foundational results and powerful techniques in representation theory: the so-called theory of purity.

Purity arises naturally in many areas of representation theory, including in the field of silting theory. The focus of silting theory is on distinguished objects determining t-structures whose hearts have particular properties and, if these objects are nice with regards to the theory of purity, then the heart has correspondingly nice properties (for example, a pure-injective cosilting object often determines a heart that is Grothendieck). The idea of this project is to introduce a new perspective on silting theory via the theory of purity and, ultimately, to develop and exploit the connection between the two topics.

Useful links

Contact details

  • Address

    Dipartimento di Informatica - Settore di Matematica
    Università degli Studi di Verona
    Strada le Grazie 15
    37134 Verona, Italy
  • Email