Postdoctoral Fellow, Mathematics - Free Boundary Problems
Carnegie Mellon University: Qatar
Location: Doha, QA
A Postdoctoral position in Mathematics is available for a research project in Carnegie Mellon University in Qatar. The research focuses on vector-valued free boundary problems, systems of variational inequalities, and interconnected partial differential equations (PDEs) arising in mathematical models with multiple interacting components. These problems appear naturally in areas such as optimal switching, mean-field game theory, multi-phase systems, and multi-membrane problems.
The appointment is for 1 year and is renewable for up to 3 years based on performance and continued funding, located in Doha, Qatar, with a preferred starting date of September 2026 or later.
Research Areas
The project will be under the supervision of Dr. Layan El Hajj and will be conducted in collaboration with leading international researchers in the field and aims to contribute significantly to a rapidly developing area of analysis and partial differential equations. The successful candidate will contribute to the development of a comprehensive mathematical framework for vector-valued free boundary problems and interconnected systems of variational inequalities. The project aims to advance the mathematical theory of vector-valued free boundary problems by investigating the existence, regularity, stability, uniqueness, and geometric properties of solutions and their associated free boundaries. Emphasis will be placed on weakly and strongly coupled systems of variational and non-variational PDEs, including settings where solutions may fail to be continuous.
About CMU in Qatar
CMU in Qatar (CMUQ) operates in concert with several other American and European branch campuses under the umbrella of Qatar Foundation's Education City (https://www.qf.org.qa/education/education-city). The branch campus closely follows the admissions requirements and English-language curriculum of the home campus in Pittsburgh, USA, which awards all degrees. The several thousand students in Education City represent a diverse international community, primarily from the Middle East, North Africa, and South Asia. CMUQ faculty include both locally appointed scholars and faculty seconded from the Pittsburgh campus. CMUQ's primary focus is undergraduate education in Business Administration, Biological Sciences, Computer Science, and Information Systems.
Qualifications
- PhD in Mathematics or a closely related field.
- Strong background in Partial Differential Equations (PDEs), Free boundary problems, Calculus of Variations, Geometric Analysis, or related areas.
- Demonstrated research potential through publications or preprints in relevant fields.
- Ability to conduct independent research and collaborate effectively within an international research team.
- Experience with free boundary problems, variational inequalities, obstacle problems, or nonlinear PDEs is highly desirable.
- Familiarity with numerical methods for PDEs, scientific computing, or computational aspects of free boundary problems is an advantage.
- Strong written and oral communication skills in English.
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