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Denmark, Aarhus – PhD Fellowship in Higher Dimensional Cluster Theory, Mathematics

Aarhus University (AU), Denmark

PhD fellowship/scholarship at Graduate School of Natural Sciences, Aarhus University, Denmark, within the Mathematics programme

Title:Higher Dimensional Cluster Theory


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General Info

Position: PhD
Fellowship/Scholarship: Natural Sciences - Aarhus University GSNS PhD Scholarships
No. of Positions: 1
Eligibility (Gender):
Eligibile Nationals: All Nationals
Research Field:
Joining Date: May, 2022
Contract Period: -

Graduate School of Natural Sciences
Department of Mathematics
Aarhus University (AU)
Aarhus C, Denmark

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Qualification Details

Applicants must have or be about to obtain a relevant MSc degree.

Responsibilities/Job Description

According to the lab interest

How to Apply?

Online Application through "Apply Now" Button from this page

Reference Number: -
(If any, use it in the necessary place)

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Documents Required

Before you apply, please read the application guide thoroughly. You can find the guide here.How to apply:

1)      Find the application form:Go to https://phd.nat.au.dk/for-applicants/apply-here/ - Note, the online application system opens on 1 December 2021.Choose February 2022 Call with deadline 1 February 2021 at midnight (23.59 CET).You will be directed to the call, and must choose the programme “Mathematics”.

2)      Fill in the following information:

  • Personal information
  • Academic background
  • Admission
  • Financing (if any): Please choose AU funds
  • Study: In the dropdown menu you must choose the project: “Higher Dimensional Cluster Theory (HiDClT)”
  • Source (how you found out about the call)

Next to some of the information fields you will find a number. Click on the number to get further directions on how to fill in the information field/what information is needed.

3)      Application attachments:Please be aware that you cannot submit the application if one or several of these documents have not been uploaded.

If you wish to upload more than one document under each section, you must scan/merge all documents into one large PDF file and upload this. Please note that we reserve the right to remove scientific papers, large reports, theses and the like. Instead you can indicate a URL where the information is available.

All information in the application must be in English or Danish, preferably English. A certified English translation is required for documents written in languages other than English or one of the Scandinavian languages (i.e. Norwegian, Swedish or Danish) languages.

As a minimum, all applications must include (pdf-files only, max. 20 MB, and no zip):

  • Curriculum vitae,
  • Motivation (max. 1 page)
  • One reference (template for references)
  • Transcripts, grade point averages (weighted and unweighted), and diploma(s) for both Bachelor’s and Master’s degree. If the original documents are not in English or one of the Scandinavian languages (i.e. Norwegian, Swedish or Danish) then copies of the original documents as well as a certified English translation must be attached.
  • Project description (½-4 pages). For technical reasons, you must upload a project description. When - as here - you apply for a specific project, please simply copy the project description above, and upload it as a PDF in the application. If you wish to, you can indicate an URL where further information can be found. Please note that we reserve the right to remove scientific papers, large reports, theses and the like.
  • Documentation of language skills if required.

After submission of the application, you will receive a confirmation e-mail with an application ID, you should use for reference if needed.

About the Natural Sciences - Aarhus University GSNS PhD Scholarships

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About the Project

Project description: Classic cluster theory concerns cluster algebra, cluster categories, and their many interactions.  It is controlled by two-dimensional combinatorial structures like triangulations of surfaces.  This proposal will generalise cluster theory to higher dimensions with the key aim of defining higher dimensional cluster algebras.  The methodology builds on known examples of higher dimensional cluster categories and tropical friezes.  Such higher cluster categories are key examples of d-angulated categories, and the project has an extensive interface with the wider area of higher dimensional homological algebra.

The proposal consists of three independent projects: (Dynkin), (RepFin), and (Surface). Project (Dynkin) concerns the higher dimensional generalisation of cluster theory to Dynkin type A; it offers a selection of concrete examples open to computational methods.  Project (RepFin) concerns the generalisation to d-representation finite type; several families of concrete examples are also available here, not least because 2-representation finite algebras are plentiful and well-understood.  Finally, project (Surface) concerns the cluster theory of generalised surfaces, for instance cyclic polytopes with an internal “hole”.

The proposal has potential applications in combinatorics because of its links to higher Stasheff-Tamari orders and in geometry because of the links between cluster theory and knot invariants.

About the Employer: Aarhus University (AU)

Note or Other details

The graduate school reserves the right to verify the authenticity of your educational diploma and transcripts:

  • Request additional information to verify an application.
  • Reject the application if it is proven, or if the University has reasonable belief, that the information provided is false or if the applicant refuses to provide the requested information, whether or not an offer has already been made.
  • For further information on applying, assessment procedures, etc. please see the GSNS Application Guide.

Please note:

  • The programme committee may request further information or invite the applicant to attend an interview.

All interested candidates are encouraged to apply, regardless of their personal background. Aarhus University’s ambition is to be an attractive and inspiring workplace for all and to foster a culture in which each individual has opportunities to thrive, achieve and develop. We view equality and diversity as assets, and we welcome all applicants.

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Contact details

Applicants seeking further information for this project are invited to contact:Peter Jørgensen, peter.jorgensen@math.au.dk

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