PhD in the School of Mathematics and Statistics - A project in Higher Dimensional Homological Algebra – novel combinatorial structures to homological algebra and representation theory

Number of awards:
1

Start date and duration:
September 2017

Overview:
The School of Mathematics and Statistics is pleased to announce that a fully-funded PhD studentships in Higher Dimensional Homological Algebra is available, commencing in September 2017.

The successful candidate will join the research group of Professor Peter Jorgensen who will be the main supervisor.

A more detailed description of the research group and the project can be found at https://sites.google.com/site/nclhha/.

The successful candidate will also be given the opportunity to complete teaching and demonstrating duties within the school amounting to up to £1500 per annum.

Interested applicants are encouraged to email Professor Peter Jorgensen ([Email Address Removed])

Classic homological algebra had its origin some 60 years ago in algebraic topology. Since then, it has grown to a theory with applications to many areas of mathematics, including combinatorics, geometry, and representation theory. Classic homological algebra is often phrased as the theory of abelian and triangulated categories.

Higher dimensional homological algebra is a new development of the last decade, first introduced by Iyama. It is the theory of d-abelian categories, as defined by Jasso [2], and (d+2)-angulated categories, as defined by Geiss, Keller, and Oppermann [1], where d>0 is an integer. In these categories, the role previously played by 1-extensions is taken over by d-extensions. Note that the case d=1 gives ordinary abelian and triangulated categories, hence classic homological algebra. We refer to (d+2)-angulated categories because the case d=1 gives triangulated categories.

Higher dimensional homological algebra is currently very active. It has applications to algebraic geometry, combinatorics, and the representation theory of finite dimensional algebras. Some of the combinatorial structures which appear, like higher dimensional cyclic polytopes in the work by Oppermann and Thomas [3], are novel to homological algebra and representation theory.

Sponsor:
School of Mathematics and Statistics (http://www.ncl.ac.uk/maths/).

Name of supervisor(s))
The project will be supervised by Professor Peter Jorgensen (http://www.ncl.ac.uk/maths/staff/profile/peterjorgensen.html#research).

Eligibility Criteria:
This studentships is available to UK/EU and International candidates, who have/expect to achieve a 2:1 honours degree in Mathematics or another strongly quantitative discipline, or an international equivalent.

Applicants whose first language is not English require a minimum of IELTS 6.5. International applicants may require an ATAS (Academic Technology Approval Scheme) clearance certificate prior to obtaining their visa and to study on this programme.

How to apply:
You must apply through the University’s online postgraduate application form (http://www.ncl.ac.uk/postgraduate/apply/). All relevant fields should be completed, but fields marked with a red asterisk must be completed.

Please include the following information:
•Insert the programme code 8080F in the programme of study section
•Select PhD Mathematics – Statistics- Pure Mathematics
•Insert the studentship code MS032 in the studentship/partnership reference field.
•Attach degree transcripts and certificates, and if English is not your first language, a copy of your English Language qualification
•Attach a covering letter and CV, the letter must clearly state the project name and the code MS032.