Master projects, Franz Luef
The following master projects are possible places to start from, but in case you have an idea outside the scope of these suggestions, please contact me for further discussion. My interests are wide-spread and range from applied to pure mathematics and also include topics in mathematical physics. More specific, I have been working on problems in noncommutative geometry, harmonic (Fourier) analysis, time-frequency analysis, frames for Hilbert spaces and Hilbert C*-modules, pseudodifferential operators, symplectic geometry and uncertainty principles, time-frequency analysis, sigma models on noncommutative spaces, deformation quantization and modulation spaces. Here are a few potential topics for master projects, but there is no problem to develop a project topic given the indivdual interests of someone interested in analysis.
Theoretical aspects of wireless communication
Some aspects of wireless communication are based on Gabor frames, a generalization of orthonormal bases, a better understanding of these are of interest to applied and pure mathematicians. There are a number of problems and topics around this circle of ideas that are accessible for students of engineering, mathematics or physics programs.
Noncommutative geometry is an interesting extension of Riemannian geometry with links to physics and engineering. In my research I have focused on the Moyal plane and noncommutative tori, two well-studied noncommutative manifolds. Topics in this area are of a broad nature, ranging from problems based on Fourier analysis to algebra and function spaces.
Mathematical aspects of quantum mechanics
Uncertainty principles, quantization, quantum integer Hall effect, almost Mathieu operators are topics of interest and accessible to a wide range of students.