PhD student position in mathematics for deep learning foundations

at Chalmers University of Technology
Published January 19, 2023
Location Gothenburg, Sweden
Category Deep Learning  
Job Type Scholarship  


Information about the division and the department
The Department of Mathematical Sciences at Chalmers University of Technology and the University of Gothenburg has about 200 employees, and is the largest department of mathematics in Sweden. The department has three scientific divisions, Algebra and Geometry, Analysis and Probability Theory, and Applied Mathematics and Statistics, and conducts successful research in pure and applied mathematics and mathematical statistics in a wide range of research areas.  We are located in a modern building at the center of the Chalmers campus. More information about us can be found on our website

At the division Algebra and Geometry we conduct research within the scope of algebraic- and complex geometry, various aspects of number theory, algebra and representation theory, complex analysis, mathematical physics and 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 grand challenges. The center Wallenberg AI, Autonomous Systems and Software Program (WASP) is  running a program to develop the mathematical side of this area, see The aim is to promote the competence of Sweden as a nation within the area of AI.

We are taking part in this program through the following research project:
- Mathematics for the foundations of deep learning: Geometric Deep Learning and Neural Tangent Kernels
Supervisor: Jan Gerken (Department of Mathematical Sciences)

Project description
Deep learning is an incredibly successful machine learning technique in areas ranging from computer vision to natural language processing. However, despite its success, little is understood about the theoretical foundations of deep learning, impeding progress in applications and research alike. It is therefore imperative to develop an understanding of the mathematical structures underlying deep learning. The PhD project will address this from the point of view of group theory combined with insights from theoretical physics, building on recent advances in the highly active areas of geometric deep learning and neural tangent kernels. Possible further topics concern the geometries of data and of probability distributions as well as the application of deep learning to research in pure mathematics.

The questions investigated in this project find applications in many important areas such as computer vision, quantum chemistry, condensed-matter physics and explainable AI and collaborations in these areas exist within the group.

Nomination process
We are seeking a PhD student to be nominated for participation in the graduate school in the mathematics relevant to AI that will be organized by WASP. The final selection of the candidate will then be done by the board of WASP. The project is expected to start on August 15, 2023, but the starting date is flexible.

Major responsibilities
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. You will also be enrolled in a graduate program in the Department of Mathematical Sciences. You will furthermore be part in a national research school, WASP AI/math, with a joint course package, yearly winter-meetings and the possibility to interact with leading researchers in the field. 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�partmental work, mostly teaching duties.

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. They 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.

Experience in some of the following areas is meritorious: quantum field theory, group theory, statistics, neural networks, machine learning and programming.

It is important that you mention in the application your specific research interests. You should also include all relevant work such as bachelor's or master's thesis and articles (provide an English summary if necessary) that you have authored or co-authored.  Evidence of problem solving skills is significant, besides course grades.

As Chalmers is a highly international enviroment, proficency in written and spoken English is necessary.

Contract terms
Full-time temporary employment. The position is limited to a maximum of five years.

We offer
Chalmers offers a cultivating and inspiring working environment in the coastal city of Gothenburg.
Read more about working at Chalmers and our benefits for employees.

Chalmers aims to actively improve our gender balance. We work broadly with equality projects, for example the GENIE Initiative on gender equality for excellence. Equality and diversity are substantial foundations in all activities at Chalmers.

Application procedure
The application should be marked with Ref 20230018 and written in English. The application should be sent electronically and be attached as PDF-files, as below. 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, Ref. number)
• CV
• Other, for example previous employments or leadership qualifications and positions of trust.
• Two references that we can contact.

Personal letter: (Please name the document as: Personal letter, Family name, Ref. number)
1-3 pages where you:
• Introduce yourself
• Describe your previous experience of relevance for the position (e.g. education, thesis work and, if applicable, any other research activities)
• Describe your future goals and future research focus

Other documents:
• Copies of bachelor and/or master’s thesis.
• Attested copies and transcripts of completed education, grades and other certificates, e.g. TOEFL test results.

Please use the button at the foot of the page to reach the application form.

Application deadline: February 24,2023

For questions, please contact:
Daniel Persson, head of unit
Tel: 031-7723174

Jan Gerken, project leader

*** Chalmers declines to consider all offers of further announcement publishing or other types of support for the recruiting process in connection with this position. ***

Chalmers University of Technology conducts research and education in engineering sciences, architecture, technology-related mathematical sciences, natural and nautical sciences, working in close collaboration with industry and society. The strategy for scientific excellence focuses on our six Areas of Advance; Energy, Health Engineering, Information and Communication Technology, Materials Science, Production and Transport. The aim is to make an active contribution to a sustainable future using the basic sciences as a foundation and innovation and entrepreneurship as the central driving forces. Chalmers has around 11,000 students and 3,000 employees. New knowledge and improved technology have characterised Chalmers since its foundation in 1829, completely in accordance with the will of William Chalmers and his motto: Avancez!