PhD position in Mathematics focusing on complex geometry and optimal transport - 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 focusing on complex differential geometry and optimal transport. The position covers four years of third-cycle studies, including participation in research and third-cycle courses. The last day to apply is June 10, 2024.

This recruitment is part of larger expansion of the research group in Geometry. The group, which currently consists of five senior researchers, three doctoral students and one postdoc, constitute a young environment with an inclusive and friendly atmosphere and during the following year it will increase in size by three doctoral students and three postdocs.

Project description and tasks
In the 80’s and 90’s a surprising phenomenon was observed by physicists: It seemed like certain complicated geometric objects (Calabi-Yau manifolds) appeared in pairs, one taking the form of a mirror image of the other. The phenomenon was dubbed mirror symmetry and similarly as for other duality principles in mathematics, for example the duality of time and frequency in Fourier analysis, researchers quickly realized it could be very useful. An important branch of research with the aim of understanding mirror symmetry is the SYZ-conjecture, which gives a detailed description of a conjectural structure in Calabi-Yau manifolds. To show that this description is true has turned out to be very difficult. In essence, the problem consists of controlling the limit of solutions to certain (Monge-Ampère) partial differential equations when the dimension of their domain drops, which is a very challenging problem in general. However, due to a recent breakthrough the problem has been reduced to showing existence of solutions to a class of these equations in very singular settings. The purpose of this project is to show existence of these solutions and study their properties to learn more about mirror symmetry. The main new idea is to use optimal transport to achieve this. Optimal transport is a classical tool with roots in 18th century France, where it was studied in relation to engineering and geometry. Here, it will provide a link between the partial differential equations above and a very robust variational theory which, as indicated by preliminary results, might be very useful. 

The doctoral student will carry out research in complex algebraic geometry and optimal transport as part of the project above, which is funded by the Swedish Research Council. As part of this, they will write articles (both as single author and in collaborations) and publish in international journals. The project will also present many opportunities to travel and take part in conferences and workshops with possibilities to initiate collaborations with researchers at other universities, both in Sweden and internationally. Upon completion of their doctoral degree, they will be in a good position to apply for national and international postdoc grants, for example the Mathematics Program by the Knut and Alice Wallenberg Foundation or the Marie Skłodowska-Curie Postodctoral Scholarships by the European Research Council. 

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.

The ability to communicate in written and spoken English is required. The doctoral student is expected to take on an active role in the research project and in institutional work. They should have a scientific mindset, and ability to work independently, and be structured, flexible and solution oriented. Above all, the doctoral student should be determined to continuously develop their skills and contribute to the research project. Prior experience with complex differential or algebraic geometry, partial differential equations or optimization is beneficial, but not a requirement. 

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 January 2025 or by agreement. 

The position is a salaried position. Therefore, the doctoral 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 June 10, 2024. 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.
• 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 and non-binary applicants.

We welcome applications from candidates with disabilities and provides adjustments to ensure that anybody can participate fully in the selection process. If you need an adjustment when accessing the application form, attending interviews, or for any other part of the application process, please contact Jakob Hultgren (jakob.hultgren@umu.se) or equal opportunitys representative Lars-Daniel Öhman (lars-daniel.ohman@umu.se). Adjustments can include for example:

• additional support to complete the application form.
• technical support during interviews for candidates with hearing or visual impairments.
• support during interviews for neurodiverse candidates and those with mental health conditions, for example the possibility of receiving some of the interview questions beforehand.
• adjustments for those candidates requiring a chaperone during interviews.

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 the position: Jakob Hultgren, Associate Professor, Jakob.hultgren@umu.se

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