C – Geometric structures and high dimensional problems

Many recent challenges in materials science, in data mining, or in vision are linked to very high or even infinite dimensional and nonlinear phenomena. However, the major characteristics and the underlying driving mechanisms can be described on lower dimensional geometric structures. Such low dimensional geometric descriptions also appear in the mathematical study of transport phenomena, dispersive dynamics and sharp estimates in harmonic analysis. Project Group C is dealing with the identification, the analysis, and the numerical approximation of emerging geometric structures in high dimensional spaces.

 

C01 Wasserstein geometry, Ricci curvature and geometric analysis (Kopfer, Sturm)
C03 Nonlinear dispersive equations (Koch)
C04 Multilevel sparse tensor product approximation for manifolds and for functions and operators on manifolds (Griebel)
C05 Discrete Riemannian calculus on shape space (Rumpf)
C06 Numerical optimization of shape microstructures (Conti, Rumpf)
C08 Multilinear estimates in geometric Fourier analysis (Thiele)
C10 Sparse controls in optimization of quasilinear partial differential equations (Neitzel)