项目介绍

2025年4月19日

Are you passionate about mathematics and looking to embark on a journey of discovery? The Division of Algebra and Geometry is seeking a highly motivated PhD student to join our team.

We seek a PhD student for a project at the intersection of mathematics and deep learning to work on theoretical aspects of geometric deep learning. The question whether more data and compute are sufficient to improve neural networks is highly debated at the moment in all areas of deep learning. In this project, you will work on a theoretical framework which will help to better understand these questions in the context of geometric deep learning and add rigorous arguments to a debate driven by empirical results.

Who we are looking for
We seek candidates with the following qualifications:

• To qualify as a PhD student, you must have obtained a master’s degree or a 4-year bachelor’s degree (or expect to complete such a degree by the starting date of the position) in relevant field. 
• Applicants must have a strong background in mathematics, theoretical physics or computer science.
• Some programming experience is compulsory and the applicants should be keen to develop their programming- and software development skills. 
• Strong written and verbal communication skills in English

Experience in some of the following areas is meritorious: group theory, statistics, neural networks, machine learning and programming. Evidence of problem solving skills is significant, besides grades.

Research environment
In the GAPinDNNs research group on Geometry, Algebra and Physics in Deep Neural Networks at the division of Algebra and Geometry, we conduct research on deep learning, in particular geometric deep learning and mathematics for AI.

The expansion of Artificial Intelligence (AI), in the broad sense, is one of the most exciting developments of the 21st century. This progress opens up many possibilities but also poses challenges.

Wallenberg AI, Autonomous Systems and Software Program (WASP) is Sweden’s largest individual research program ever, a major national initiative. The vision of WASP is excellent research and competence in artificial intelligence, autonomous systems and software for the benefit of Swedish society and industry. Read more: https://wasp-sweden.org/

We are taking part in this program through the following research project:

How Do Neural Networks Learn Symmetries? Augmentation, Randomization and Equivariance

Supervisor: Jan Gerken (Department of Mathematical Sciences) 
 
Project description
In many deep learning applications ranging from medical image analysis to quantum chemistry, the symmetries of the underlying problem pose an important constraint. These can be taken into account by modifying the architecture of the network (yielding so-called equivariant neural networks) or by learning the symmetry from the data (data augmentation). In this project, the aim is to construct a theoretical framework for data augmentation of deep neural networks. During the last year, the debate around the trade-offs between data augmentation and manifest equivariance has intensified, with data augmentation gaining popularity in notable domains such as protein design and quantum chemistry. The goal of this project is to contribute to this debate with a theoretical framework and novel algorithms.

This project will be conducted in close collaboration with Axel Flinth from Umeå University (who will act as WASP co-supervisor) and Pan Kessel from the company Genentech Roche in Basel (who will act as industrial supervisor).

About the department of Mathematical Sciences

Join one of Sweden’s leading mathematics departments!

The Department of Mathematical Sciences at Chalmers University of Technology and the University of Gothenburg is the largest mathematics department in Sweden, with around 200 dedicated employees. We excel in both pure and applied mathematics as well as mathematical statistics, with research spanning a wide range of areas.

Our department is organized into three vibrant divisions:

• Algebra and Geometry
• Analysis and Probability Theory
• Applied Mathematics and Statistics

If you are looking for an inspiring place to advance your career in mathematics, join us and be part of a community that values innovation, collaboration and inclusion.

What you will do
As a PhD student you will be part of an international research environment while you expand your knowledge of the field and write your thesis. This gives opportunities for many inspiring conversations, a lot of autonomous work and some travel. You are expected to develop your own ideas and communicate scientific results orally as well as in written form. In addition, the position will normally include 20% departmental work, mostly teaching duties. You will also take courses at an advanced level within one of the gradite schools at the Depratment of Mathematical Sciences. You will also become part of the national WASP gradute school which includes courses, international study trips and conferences and join the local community of WASP students at Chalmers.

Contract terms and what we offer

• The PhD-position is fully funded from the start
• As a PhD student at Chalmers, you are an employee and enjoy all employee benefits. Read more about working at Chalmers and our benefits for employees.
• The position is limited to four years, with the possibility to teach up to 20%, which extends the position to five years.
• A dynamic and inspiring working environment in the coastal city of Gothenburg.
• A starting salary of 34,550 SEK per month (valid from May 25, 2025).

Chalmers is dedicated to improving gender balance and actively works with equality projects, such as the GENIE Initiative for gender equality and excellence. We celebrate diversity and consider equality and inclusion as fundamental aspects of all our activities.

If Swedish is not your native language, Chalmers offers Swedish courses to help you settle in. If you need to move to Gothenburg for this position, you have the option to rent accommodation from the University of Gothenburg for the duration of one year.

Nomination process:
We are seeking a PhD student to be nominated for participation in the WASP graduate school. The final selection of the candidates will then be done by the board of WASP.  The project is expected to start on August 15, 2025, but the starting date is flexible.  

Discover more
Find more general information about doctoral studies at Chalmers here. 

Application procedure
The application should be written in English. Attach the following documents as PDF-files. Maximum size for each file is 40 MB. Please note that the system does not support Zip files.

• CV: (Please name the document: CV, Family name)
• Personal letter
• Two references that we can contact
• Transcripts from all Bachelor’s and Master’s programs you took or are currently taking
• Master’s thesis if available and in English, alternatively a 1-page summary of your thesis project
• If available: documents confirming your English proficiency: e.g. TOEFL/IELTS test results

It is important that you mention in the application your specific research interests.

Use the button at the foot of the page to reach the application form. 

Please note: The applicant is responsible for ensuring that the application is complete. Incomplete applications and applications sent by email will not be considered.

Application deadline:  21 May 2025

For questions please contact: 
Jan Gerken, Main Supervisor, gerken@chalmers.se
Daniel Persson, Head of Unit, Algebra and geometry, daniel.persson@chalmers.se

We look forward to your application!