Cooperation project of the Goethe-University Frankfurt and the African Institute for Mathematical Sciences (AIMS)

Local and nonlocal effects in geometric variational problems (2017-2021)

Funding program of the German Academic Exchange Service (DAAD)

Variational principles are the mathematical key to describe many of the most fascinating phenomena in nature, and they have various applications in physics, engineering and economics. Within the class of geometric variational problems, typical examples are the shape of solid bodies with optimal thermal insulation or minimal air resistance, area minimizing surfaces with prescribed boundary properties or the shape of membranes minimizing the frequency of the n-th normal mode.

Many geometric variational problems can be formulated as optimization problems for energy functionals depending on domain shapes or, in the case of free boundaries, on shapes of domain partitions.  Applications arise in this context e.g. within the modeling of phase separation of fluids and of the formation of cracks in solids under pressure. In recent years, also nonlocal effects have been investigated in these applications via new mathematical models. Mathematically, nonlocality is an intrinsic feature of integral operators and associated energy functionals. In the context of functional variational principles and associated inequalities, nonlocal energy functionals are receiving immense attention currently as they are closely related to problems in quantum mechanics and nuclear physics.  Somewhat surprisingly, nonlocal effects have also been detected recently in classical geometric optimization problems such as Serrin's overdetermined boundary value problem.

The cooperation project is devoted to these and related topics in the context of partial differential equations. The aim is to support junior scientists  from AIMS Senegal and other African and German research institutions. By this, we wish to strenghten the cooperation between AIMS Centers and German universities. The project consists of the following components.

PhD fellowships for highly qualified master's graduates from African universities and research institutions

This project component features grants for three PhD candidates. The fellowship runs from January 1st, 2018 to March 31st 2021, and it provides the opportunity to conduct a PhD research project at the interface of Partial Differential Equations, Geometric Variational Problems and Nonlocal Analysis.

During each of the years 2018-2021, the grants holders will stay six months (April - September) at the Goethe University Frankfurt in the research group of Tobias Weth and spend the remaining six months at AIMS Senegal in the research group of Mouhamed Moustapha Fall.

In addition to individual supervision by Prof. Fall and Prof. Weth, the grant holders are expected to participate in the scientific activities of the research group "Partial Differential Equations" at the Goethe University and of AIMS Senegal. They will be given the chance to attend selected courses (in English language) of the mathematics master program of the Goethe University. During their stays at AIMS Senegal, the fellowship holders will be encouraged to work part-time as teaching assistants or tutors within the AIMS Senegal Master Program.

Within the fellowship period, the grant holders will be given the chance to participate in three one-week spring/summer schools. Moreover, they will be asked to register for membership of the Goethe Research Academy for Early Career Researchers (GRADE) in Frankfurt which provides many helpful services and individual coaching.


Each fellowship consists of a monthly rate of 1000 € for each month spent at the Goethe University Frankfurt and 400 € for each month spent at AIMS Senegal. It also covers the travel costs of one round trip between Frankfurt and AIMS Senegal in each of the years 2018-2020 according to the regulations of DAAD.

Who can apply?

The grants are addressed at nationals of African countries which are master's graduates from African universities and research institutions (including AIMS Centers).

Applications with a strong background in the Analysis of Partial Differential Equations and/or in Geometric Analysis are preferred.

Applicants should provide evidence that their spoken and written English is adequate for an international PhD program in mathematics.

Since the program consists in alternating stays at AIMS Senegal and in Frankfurt, Germany, open-mindedness of applicants with regard to intercultural encounters is required.


Complete applications include

- a motivational letter

- a CV

- a transcript of records and university master certificate

- a copy of the master thesis (if available)

- english language certificates (if available)

The deadline for applications is

October 15th, 2017.

To apply, please send the documents listed above in pdf-format (preferably one file for the master thesis and one file for the remaining documents) to   and

Selection process

A number of short list candidates, selected by an expert committee, will be invited to a selection seminar at the Goethe-University which will take place 

December 4th and 5th, 2017.

Participant costs including travel expenses and accomodation will be covered according to the regulations of DAAD.

Schools for Junior Scientists at AIMS Senegal and at German Universities

The research program also features summer and spring schools both in Germany and at AIMS Senegal. The first school will take place in Frankfurt, Germany in September 2018. Details will be given soon.

The research program is granted by

Project ID 57385104