Hall algebras of derived categories of gentle algebras

Applications are invited for a three-year PhD studentship. The studentship will start on 1 October 2021.

To apply please use the online application form. Simply search for PhD Mathematics and Statistic, then clearly state that you are applying for a PhD studentship within the School of Engineering Computing and Mathematics and name the project at the top of your personal statement.

Online application

Take a look at the Doctoral College's general information on applying for a research degree.

Project description

Since their introduction in the 1970s, derived and triangulated categories have become an important setting in which connections between algebra, geometry and theoretical physics can be understood. However, it is often complicated to do explicit calculations. This project will focus on a class of examples from representation theory (of finite dimensional algebras), namely, the derived categories of gentle algebras.  Recent developments in this area have allowed explicit computations to be done in terms of certain ‘geometric models’ consisting of graded arcs on surfaces with boundary.

Hall algebras were classically studied in the context of group theory but were generalised to the setting of abelian categories by Ringel, and more recently to derived categories by Toën. There are however relatively few examples where these Hall algebras have been explicitly computed in terms of generators and relations. The aim of this project is to study the Hall algebras of derived categories of gentle algebras. The project will start by considering the cases of discrete derived categories of finite global dimension, which form a family of examples of derived categories of gentle algebras. It will then progress to studying more general cases.

Eligibility 

Applicants should have (at least) a first or upper second class honours degree in an appropriate subject and preferably a relevant MSc or MRes qualification. 

The studentship is supported for three years and includes full home tuition fees plus a stipend of £15,609 per annum (2021/22 rate). The studentship will only fully fund those applicants who are eligible for home fees with relevant qualifications. Applicants normally required to cover international fees will have to cover the difference between the home and the international tuition fee rates (approximately £12,697 per annum).

If you wish to discuss this project further informally, please contact Dr Nathan Broomhead (nathan.broomhead@plymouth.ac.uk). However, applications must be made in accordance with the details shown below.

General information about applying for a research degree at the University of Plymouth and to apply for this position please visit: https://www.plymouth.ac.uk/student-life/your-studies/research-degrees

Please mark it FAO Doctoral College and clearly state that you are applying for a PhD studentship within the School of Engineering, Computing and Mathematics.

For more information on the admissions process email the Doctoral College, doctoralcollege@plymouth.ac.uk.

The closing date for applications is 19 April 2021. Shortlisted candidates will be invited for interview the week beginning 3 May 2021. We regret that we may not be able to respond to all applications. Applicants who have not received an offer of a place by 31 May should consider their application has been unsuccessful on this occasion.