Applications are invited for a PhD fellowship/scholarship at Graduate School of Natural Sciences, Aarhus University, Denmark, within the Mathematics programme. The position is available from February 2022 or later.

Title:
Spatial random networks and topological data analysis on large random structures

Research area and project description:
The research area for this position is the development of asymptotic results for spatial random networks and for topological data analysis on large random structures.

In topological data analysis (TDA), invariants from algebraic topology are used to gain insights into data. TDA is now an established tool to explain the arrangement of galaxies, to classify proteins, and to statistically analyze the pore configuration in granular materials. All of these applications share a common goal: unveiling structure in massive amounts of possibly high-dimensional data.

The successful candidate will contribute to building a firm statistical foundation of TDA by developing asymptotic results in large domains such as central limit theorems, large deviation principles and Poisson approximation results. A key element will be the development of a novel form of continuum percolation that can capture higher-order interactions and will allow controlling the effect of long-range spatial correlations. The first phase of the project will be devoted to a detailed analysis of random structures in two and three dimensions. In the second phase, the experiences gathered so far will provide the basis for dealing with high-dimensional problems.

The PhD project is of high relevance since the statistical foundations of TDA are still in infancy although this methodology is now applied in a variety of fields within the natural sciences. Hence, there is also potential for work in interdisciplinary projects.

Qualifications and specific competences:
We are looking for highly motivated and creative applicants holding  (or expecting to finish soon) a Master’s degree in Mathematics, Statistics or a related field. The candidate should be able to demonstrate academic excellence through grades or recommendation letters.

The project is located at the interface between probability theory, statistics and topology. Hence, the successful candidate should have experience in at least one of these domains and be excited about learning the key techniques in the others. Having worked with random networks, interacting particle systems or asymptotic results in stochastic geometry is an advantage but not a strict prerequisite

Place of employment and place of work:
The place of employment is Aarhus University, and the place of work is Department of Mathematics, Aarhus University, DK-8000 Aarhus C., Denmark.

Contacts:
Applicants seeking further information for this project are invited to contact:
Associate Professor Christian Hirsch, c.p.hirsch@rug.nl

Application procedures

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 September 2021.
Choose November 2021 Call with deadline 1 November 2021 at noon (11.59 AM 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)
• Study: In the dropdown menu you must choose the project: “Spatial random networks and topological data analysis on large random structures (PhHiMa)”
• 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):
One reference (template for references)

• Curriculum vitae,
• Motivation (max. 1 page)
• 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.

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.