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. This event was originally planned to take place in 2020 but was postponed due to the COVID19 pandemic.
London Mathematical Society Newsletter
I am a member of the editorial board of the LMS Newsletter. If you have any idea for a features article, then please feel free get in touch with me.
Network on Silting Theory
I am a member of a European research network on silting theory, funded by the Deutsche Forschungsgemeinschaft.
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.
Preprints
Publications
- Simples in a cotilting heart
L. Angeleri Hügel, I. Herzog and R. Laking
To appear in Mathematische Zeitschrift.
arXiv - Classification of cosilting modules in type Ã
K. Baur and R. Laking
Journal of Pure and Applied Algebra, Volume 226, Issue 10 (2022).
Journal · arXiv - 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 American 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
Other materials
- The shape of a module category
R. Laking
LMS Newsletter feature article (Issue: 494 - May 2021).
PDF - Infinite-dimensional representations of algebra
R. Laking
LMS Autumn Algebra School lectures
Videos · Lecture notes
Short CV
| Dates | Place | Position |
|---|---|---|
| Dec 2021 - present | Università degli Studi di Verona, Italy | Lecturer (RtdB) |
| Apr 2021 - Nov 2021 | Università degli Studi di Verona, Italy | Postdoctoral researcher |
| Jan 2021 - Mar 2021 | Università degli Studi di Verona, Italy | Marie Skłodowska-Curie fellow |
| Oct 2020 - Dec 2021 | Hausdorff Research Institute for Mathematics, Bonn, Germany | Junior Trimester Program |
| Jan 2019 - Sept 2020 | 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 September 2020 and between January 2021 and March 2021 I was working on a project funded by the Marie Skłodowska-Curie Individual Fellowships program. The project, called Functorial Techniques in Silting Theory, aimed 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.
This project received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 797281. 
The content of this website reflects only the author's view and the Research Executive Agency (REA) is not responsible for any use that may be made of the information it contains.
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.
This project received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 797281.