The analysis of partial differential equations occupies a central place among a wide range of sciences. Whenever there are processes of evolution or static models, starting from the groundbreaking works of Isaac Newton, they are often described by partial differential equations (PDEs). The mathematical insights and understanding of solutions of such equations often help resolving fundamental problems in many different sciences: physics, engineering, finance, materials, biology, medicine, arts, humanities, social sciences.
Our project is devoted to several closely related topics in the field of Analysis & PDEs: noncommutative phase space analysis, analysis on groups, PDEs with singularities, linear and nonlinear PDEs, and fractional order PDEs. The proposed research will build upon the very recent advances and modern techniques of analysis to investigate important properties of solutions of PDEs of different types by developing the so-called phase space understanding of the underlying processes. A characteristic feature of our approach is the deep study of ‘noncommutativity’, which can be viewed as a quantum physics manifestation of the Heisenberg uncertainty principle. Apart from achieving major purely mathematical advances the project also aims at pursuing a number of concrete applications for specific previously unapproachable models described by PDEs of different types. The deep connections between mathematics and other sciences lie at the heart of this research project.
Please explore this site to know more about the work of our Odysseus group.
Project Reference: FWO Odysseus 1 grant G.0H94.18N
Objective of FWO Odysseus program:
The Odysseus program supports outstanding researchers who have built up a career outside Flanders. The program provides start-up funding in order to develop a research group within a Flemish university or to set up a research line and become progressively more involved in the Flemish research establishment.
What makes this program unique is the combination of a permanent position at a Flemish university and sufficient project funding to establish your own research team. This symbiosis forms the ideal starting point to attract high level, international research to Flanders.