📣 Help Shape the Future of UKRI's Gateway to Research (GtR)

We're improving UKRI's Gateway to Research and are seeking your input! If you would be interested in being interviewed about the improvements we're making and to have your say about how we can make GtR more user-friendly, impactful, and effective for the Research and Innovation community, please email gateway@ukri.org.

Derived Localisation in Algebra and Homotopy Theory

Lead Research Organisation: City St George’s, University of London
Department Name: Sch of Engineering and Mathematical Sci

Abstract

Abstracts are not currently available in GtR for all funded research. This is normally because the abstract was not required at the time of proposal submission, but may be because it included sensitive information such as personal details.

Publications

10 25 50
publication icon
Angeleri Hügel L (2019) Model Theory of Modules, Algebras and Categories

publication icon
Angeleri Hügel L (2020) Flat ring epimorphisms and universal localizations of commutative rings in The Quarterly Journal of Mathematics

publication icon
Angeleri Hügel L (2019) Partial silting objects and smashing subcategories in Mathematische Zeitschrift

publication icon
Angeleri Hügel L (2017) Torsion pairs in silting theory in Pacific Journal of Mathematics

publication icon
Braun C (2018) Derived localisation of algebras and modules in Advances in Mathematics

publication icon
Chuang J (2021) Maurer-Cartan Moduli and Theorems of Riemann-Hilbert Type in Applied Categorical Structures

publication icon
Chuang J (2021) Rank functions on triangulated categories in Journal für die reine und angewandte Mathematik (Crelles Journal)

publication icon
Chuang J (2018) Homotopy theory of monoids and derived localization

publication icon
Chuang J (2021) Homotopy theory of monoids and derived localization in Journal of Homotopy and Related Structures

publication icon
Chuang J (2020) Homological epimorphisms, homotopy epimorphisms and acyclic maps in Forum Mathematicum

 
Description A theory of derived rank functions has been developed, generalising the work of Cohn and Schofield, with connections to derived localisations. A prepirnt has been posted on the ArXiv and further work is in progress. A new approach to the Homological Perturbation Lemma has been introduced. This work, entitled `On the Perturbation Algebra' has been published in the Journal of Algebra. Further works `Maurer-Cartan moduli and theorems of Riemann-Hilbert type' and `Homotopy theory of monoids and derived localization' have been published in Applied Categorical Structures and in Journal of Homotopy and Related Structures. Postdoc Vitoria and collaborators have carried out research on `Torsion Pairs in Silting Theory', published in the Pacific Journal of Mathematics, `Silting and cosilting classes in derived categories', published in the Journal of Algebra, `Realisation functors in tilting theory', published in Mathematische Zeitschrift, `Properties of abelian categories via recollements', published in the Journal of Pure and Applied Mathematics, `A characterisation of t-tilting finite algebras', published in Comtemporary Mathematics, and Definability and Approximations in Triangulated Categories, to be published in Pacific Journal of Mathematics.
Exploitation Route The findings contribute to the academic sphere.
Sectors Other
 
Description Rank functions on triangulated categories, homotopy theory and representations of finite groups
Amount £393,338 (GBP)
Funding ID EP/T030771/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 03/2021 
End 08/2024