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
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
Due to the Coronavirus pandemic, the PATHS workshop has been postponed. New dates for the workshop will be announced as soon as possible.
I am one of the organisers of the FD seminar, a weekly online seminar on the representation theory of finite-dimensional algebras.
Preprints
- Classification of cosilting modules in type Ã
K. Baur and R. Laking
(Preprint, 2019).
arXiv
Publications
- Cotilting sheaves over weighted noncommutative regular projective curves
D. Kussin and R. Laking
Documenta Mathematica, Volume 25, 1029-1077 (2020).
Journal · arXiv - 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).
Journal - 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.
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.