PhD position in mathematics specialising in representation theory and number theory - Befattningen är under tillsättning eller redan tillsatt, och det är inte längre möjligt att lämna in en ansökan

The Department of Mathematics and Mathematical Statistics is opening a PhD position in mathematics specialising in representation theory and number theory. The position covers four years of third-cycle studies, including participation in research and third-cycle courses. The last day to apply is 14 May 2023.

Project description and tasks
The PhD student will carry out research in primarily representation theory, but also in number theory as part of a project supervised by Henrik Gustafsson. The main focus of the project is representations of p-adic groups where p is a prime number, and especially so-called Whittaker functions which describe these representations and frequently also appear in number theory.

Surprisingly, these functions can in several cases be computed by partition functions of exactly solvable models from statistical mechanics described by paths in a two-dimensional lattice. The fact that the lattice model is solvable means that the partition function satisfies a so-called Yang–Baxter equation related to a quantum group which we can use to derive identities for the original Whittaker function. 

The aim of the project is to explain and expand on the web of unexpected and detailed connections that have been discovered between these very different objects with applications to number theory, combinatorics and statistical mechanics.

The research is part of a new initiative in the research field of representation theory by the department and a part of the existing research group in discrete mathematics which at the moment consists of 18 people of which 3 are PhD students. The department for mathematics and mathematical statistics as a whole has about 100 employees with about 20 PhD students. There are ample opportunities for international collaborations in the project.

Qualifications
The doctoral student will be admitted to the third-cycle programme in the subject Mathematics. To fulfil the general entry requirements, the applicant must have qualifications equivalent to a completed degree at second-cycle level or completed course requirements of at least 240 ECTS credits, including at least 60 ECTS credits at second-cycle level. To fulfil the specific entry requirements to be admitted for studies at third-cycle level in mathematics, the applicant is required to have completed at least 60 ECTS credits within the field of mathematics, of which at least 15 ECTS credits shall have been acquired at second-cycle level. Applicants who have acquired largely equivalent skills in some other system, either within Sweden or abroad, are also eligible.

Good communication skills in both written and spoken English are required. 

Experience in representation theory, number theory or programming is beneficial, but not a requirement for the position.

As a PhD student you are expected to take an active role in the project and the department. You are expected to have a scientific approach and good collaborative skills while still being able to work independently. You should have a strong drive to continuously develop your own skills and to become an independent researcher.

The assessment of applicants is based on their qualifications and ability to benefit from the doctoral study they will receive.

About the employment
The position is intended to result in a doctoral degree. The main task of doctoral students is to pursue their third-cycle studies, including active participation in research and third-cycle courses. The duties may include teaching or other departmental work, although duties of this kind may not comprise more than 20 per cent of a full-time post. The employment is for a fixed term of four years full-time or up to five years when teaching part-time. Salary is set according to the salary ladder for PhD positions at Umeå University. Employment commences in the autumn of 2023 or by agreement. 

The position is a salaried position. Therefore, the PhD student will get access to employment benefits, such as paid parental or sick leave. See https://www.umu.se/en/work-with-us/benefits/ for some general information about benefits.

Application
Applications will be accepted via our recruitment system. The deadline for applications is 14 May 2023. Log in and apply via the button at the bottom of the page. The application must include the following documents written in English or Swedish:

• A cover letter briefly describing your qualifications and research interests, an explanation of why you are applying for the position and why you feel your qualifications and experience are relevant. If you have any of the especially mentioned merits (experience in representation theory, number theory or programming) then specify these in the cover letter.
• Curriculum vitae.
• Authenticated copies of degree certificates, diplomas or equivalent, including documentation of completed academic courses, received grades, and other certificates.
• Copies of relevant work such as master’s thesis or articles you have authored or co-authored. If the master’s thesis has not been completed before the application deadline, a summary of the master’s thesis project and current progress shall be included. The summary can, at most be five pages, including figures and references.
• Your GMAT (or GRE) and TOEFL/IELTS test scores if available.
• Contact details for at least two references.

The Department of Mathematics and Mathematical Statistics values the qualities that gender balance brings to the department. We are therefore particularly keen to hear from female applicants.

Pursuant to Chapter 12 Section 2 of the Swedish Higher Education Ordinance (SFS 1993:100), the decision regarding the position cannot be appealed.

Additional information
Additional information about Henrik Gustafsson's research:
https://hgustafsson.se

Further information about the Department of Mathematics and Mathematical Statistics:
https://www.umu.se/en/department-of-mathematics-and-mathematical-statistics/

Contact information for other information:
Henrik Gustafsson, Assistant professor henrik.gustafsson@umu.se or
Åke Brännström, Professor, Head of the Department ake.brannstrom@umu.se.

Information about getting established:
https://www.umu.se/en/work-with-us/establish-in-umea-sweden/