# 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

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.