Oberseminar Analysis Summer 2026

In this talk, we will discuss pattern formation in variational models for biological membranes, motivated by lipid raft formation. As a starting point, we consider an approximation of a two-phase Canham-Helfrich functional and present a scaling law for the minimal energy. A central ingredient in the lower bound is a class of new nonlocal and nonlinear interpolation inequalities, which control fractional Sobolev seminorms in terms of Modica-Mortola-type energies. Motivated by the scaling law, we then study a related functional with competing local and nonlocal terms and indicate results and open questions concerning the structure of minimizers. The talk is based on joint work with Barbara Zwicknagl and Janusz Ginster, and on ongoing work with Sara Daneri and Eris Runa.

Model order reduction is a field of mathematics that deals with the complexity reduction of mathematical models in order to reduce the computational costs of tasks such as numerical simulation, optimization, or control. In this talk, first an overview of the field will be given and two of the classical systems theoretic reduction methods (balanced truncation and IRKA) will be reviewed. The second part of the presentation will focus on structure-preserving reduction methods for structured models. This includes a variant of balanced truncation for symmetric second-order systems and a rational fitting method for the class of port-Hamiltonian systems. If time allows, recent directions in the direction of kernel methods will be presented.

TBA.

TBA.

TBA.

TBA.