Homological algebra of Feynman graphs
Lead Research Organisation:
City, University of London
Department Name: Sch of Engineering and Mathematical Sci
Abstract
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Organisations
People |
ORCID iD |
| Joseph Chuang (Principal Investigator) |
Publications
Braun C
(2015)
Unimodular homotopy algebras and Chern-Simons theory
in Journal of Pure and Applied Algebra
Braun C
(2014)
Homotopy BV algebras in Poisson geometry
in Transactions of the Moscow Mathematical Society
Braun C
(2013)
Unimodular homotopy algebras and Chern-Simons theory
Braun C
(2018)
Derived localisation of algebras and modules
in Advances in Mathematics
Braun C
(2013)
Homotopy BV algebras in Poisson geometry
Chuang J
(2016)
Cocommutative coalgebras: homotopy theory and Koszul duality
in Homology, Homotopy and Applications
Chuang J
(2012)
Combinatorics and Formal Geometry of the Maurer-Cartan Equation
in Letters in Mathematical Physics
Chuang Joe
(2012)
Free resolutions of algebras
in arXiv e-prints
Chuang Joseph
(2016)
ON THE MAGNITUDE OF A FINITE DIMENSIONAL ALGEBRA
in THEORY AND APPLICATIONS OF CATEGORIES
Sultana N
(2022)
Job insecurity and mental health related outcomes among the humanitarian workers during COVID-19 pandemic: a cross-sectional study.
in BMC psychology
| Description | The area of the proposed research is at the junction of several branches of pure mathematics and mathematical physics. It follows the pattern of applying the physical intuition and ideas to solving mathematical problems which has been a characteristic feature of many groundbreaking developments in algebra in geometry in the last two decades. The main discovery thus far has been a theory of derived localisation for algebras developed with A Lazarev and C Braun. The theory has applications in diverse areas, e.g. topology, homotopical algebra and geometry. A paper entitled `Derived Localisation of Algebras and Modules' has been published in Advances in Mathematics. Another thread of the project has focused on developing the homotopy theory of coalgebras. Two papers with A Lazarev and W Mannan written on the subject will appear in the journals Homology, Homotopy, and Applications, and Journal of Noncommutative Geometry. A projected started long ago with A King on free resolutions of algebras was completed, with help from the insight gained from the homotopy theory of coalgebras. |
| Exploitation Route | The theory of derived localisation of algebras will be generalised to categories. It will then have further applications, e.g. to the classification of thick subcategories in derived module categories and to fusion systems over finite p-groups. |
| Sectors | Other |
| Description | The proposed research project belongs to the realm of pure mathematics. As such, it is expected to have impact within the academic community only, at least in the foreseeable future. |
| First Year Of Impact | 2012 |
| Sector | Other |
| Description | Standard Research |
| Amount | £347,963 (GBP) |
| Funding ID | EP/N016505/1 |
| Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
| Sector | Public |
| Country | United Kingdom |
| Start | 04/2016 |
| End | 03/2019 |