## PhD projects

The RTG π^{3}comprises 12 PhD projects within and on the interface between the 3 research areas.

### R1 Inverse problems

- R1-1: Sparsity constrained parameter identification for dynamic wave scattering problems
- PI: Armin Lechleiter
- R1-2: Sensitivity of Tikhonov minimisers with respect to norm and tolerance
- PI: Iwona Piotrowska-Kurczewski
- R1-3: Efficient and reliable discretisation of primal and adjoint operators
- PI: Alfred Schmidt
- R1-4: Identification of defects in electromagnetic surface structures
- PI: Armin Lechleiter

### R2 Direct optimisation

- R2-1: Parameter identification by decomposition of non-linearities
- PI: Christof Büskens
- R2-2: Coherent discretization for adjoint operators and sparsitiy constraints
- PI: Peter Maass
- R2-3: Non-linear dynamics and parameter identification
- PI: Jens Rademacher
- R2-4: Online optimal parameter identification in dynamic controlled environments
- PI: Christof Büskens

### R3 Mathematical data analysis

- R3-1: Feature recognition using topological data analysis
- PI: Dmitry Feichtner-Kozlov
- R3-2: Equivalence between sparsity constrained NMF methods and k-means clustering
- PI: Peter Maass
- R3-3: Feature extraction by geometric harmonic analysis
- PI: Emily King
- R3-4: Adaptive and non-adaptive designs for the prospective evaluation of classification methods
- PI: Werner Brannath