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 August 2026 or later.
Title:
Kernel Embeddings for Disease Prevention
Research area and project description:
This project seeks to integrate two recently developed approaches to data analysis. The first method, introduced by the Japanese researcher Yuka Hashimoto and collaborators, applies concepts from operator algebras—particularly the theory of Hilbert C*-modules—to the study of concrete datasets. Their work suggests that this framework can capture structural attributes such as continuity and differentiability in certain classes of data more effectively than many traditional statistical techniques.
The second method builds on the celebrated Johnson–Lindenstrauss lemma, employing random projections to map high-dimensional datasets into spaces of significantly lower dimension while largely preserving their essential geometric and statistical properties. This dimensionality reduction has become a powerful tool in modern data analysis due to its efficiency and theoretical robustness.
By combining these two approaches, we expect to develop statistical methods that retain the structural sensitivity of the framework proposed by Hashimoto and co-authors, while achieving greater computational tractability and conceptual simplicity. We anticipate that this synthesis will broaden the applicability of operator-algebraic techniques and offer new insights into complex datasets.
The methods developed in the project will ultimately be applied to real-world data, including twin studies, with the broader aim of improving our understanding of factors involved in the prevention of certain forms of cancer.
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Qualifications and specific competences:
Applicants must have a relevant Master’s degree or at least one year of Master’s degree studies in either mathematics or statistics. The successful applicant should possess a solid foundation in basic statistics together with some familiarity with fundamental functional analysis—or, alternatively, a strong grounding in functional analysis complemented by introductory knowledge of statistics
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, Ny Munkegade 118, 8000 Aarhus C., Denmark.
Contacts:
Applicants seeking further information for this project are invited to contact: Associate professor Steen Thorbjørnsen, steenth@math.au.dk
How to apply:
For information about application requirements and mandatory attachments, please see the Application guide. Please read the Application guide thoroughly before applying.
When ready to apply, go to https://phd.nat.au.dk/for-applicants/apply-here/ (Note, the online application system opens 1 March 2026)
Please note:
At the Faculty of Natural Science at Aarhus University, we strive to support our scientific staff in their career development. We focus on competency development and career clarification and want to make your opportunities transparent. On our website, you can find information on all types of scientific positions, as well as the entry criteria we use when assessing candidates. You can also read more about how we can assist you in your career planning and development.
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. All interested candidates are encouraged to apply, regardless of their personal background.
