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. 

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.

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 AI: geometric deep learning and equivariant transformers


Main supervisor: Daniel Persson, Chalmers
Assistant supervisor: Jan Gerken, Chalmers
Industrial supervisor: Christoffer Petersson, Zenseact and Chalmers

Project description:
Despite the overwhelming success of deep neural networks we are still at a loss for explaining exactly why deep learning works so well. One way to address this is to explore the underlying mathematical framework. A promising direction is to consider symmetries as a fundamental design principle for network architectures. This can be implemented by constructing deep neural networks that are compatible with a symmetry group G that acts transitively on the input data. This is directly relevant for instance in the case of spherical signals where G is a rotation group. In practical applications, it was found that equivariance improves per-sample efficiency, reducing the need for data augmentation. Group equivariance has successfully been implemented in convolutional neural networks.

Recently, transformer networks have increased in popularity, in particular with impressive results both in natural language processing and computer vision. The goal of the present project is to explore equivariance in the context of transformers. This entails developing the underlying mathematical theory of equivariant transformers, as well as to consider applications in image processing, such as for example in cosmology, medical imaging or autonomous driving (e.g. fisheye camera images).

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 in the fall of 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% departmental work, mostly teaching duties.

Position summary
The employment is a fixed-term position limited to a maximum of five years, four years of studies 
and up to one year of departmental work distributed during the whole employment period.

Applicants must have a strong background in mathematics, theoretical physics or computer science. 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: group theory, representation theory, differential geometry, and machine learning, in particular programming with PyTorch or TensorFlow.

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.   

Chalmers continuously strives to be an attractive employer. Equality and diversity are substantial foundations in all activities at Chalmers.

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

We offerChalmers 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 20230312 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: [2023-06-04]

For questions, please contact:
Daniel Persson, head of unit and project leader, 031-7723174  

*** 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!

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