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New examples of fractional Calabi-Yau algebras (GRANTJ_U21SF)

School of Mathematics

About the Project

Calabi-Yau algebras are very important in mathematics: as well as turning up naturally in representation theory and topology, they are noncommutative examples of Calabi-Yau varieties which play a central role in string theory. Lately, fractional Calabi-Yau algebras have risen in prominence. These are a more restrictive class of algebras which have very good homolgical properties. They connect abstract algebra, category theory, and noncommutative geometry. They can often be described using quivers (directed graphs) together with relations. 


The aim of this project is to construct a variety of new examples of these algebras. Particular tools include the methods of higher homological algebra, as well as methods inspired by mathematical physics.  This project would suit a student who likes abstract algebra, but is also interested in explicit computations. There are possibilities to use computer software in the research if that is of interest to the candidate. 


It may be possible to undertake this PhD project on a part time basis but applicants should discuss with Dr Grant in the first instance 

For more information on the supervisor for this project, please go here

The type of programme is a PHD

Start date of the project is 1st October 2021

The mode of study is full time or part time

Funding Notes

This PhD project is offered on a self-funding basis. It is open to applicants with funding or those applying to funding sources. Details of tuition fees can be found at View Website
A bench fee is also payable on top of the tuition fee to cover specialist equipment or laboratory costs required for the research. Applicants should contact the primary supervisor for further information about the fee associated with the project.
Entry Requirements are 2:1 in Mathematics, or a degree in a mathematical subject (e.g., natural science, physics, computer science) including some study of pure mathematics


i) R. Schiffler, Quiver Representations, Springer, 2014
ii) M. Herschend and O. Iyama, n-representation-finite algebras and twisted fractionally Calabi-Yau algebras, Bull. Lond. Math. Soc. 43 (2011), no. 3, 449-466.
iii) B. Keller, Calabi-Yau triangulated categories, Trends in representation theory of algebras and related topics, 467-489, EMS Ser. Congr. Rep., Eur. Math. Soc., Zurich, 2008
iv) J. Grant, Serre functors and graded categories, arXiv:2007.01817, 2020

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