Zuvor findet um 16:45 Uhr die Teerunde in Raum 244 des Mathematikgebäudes (S2|15) Schlossgartenstr. 7, statt.
Prof. Melanie Rupflin, University of Oxford
Many interesting geometric objects are characterised as minimisers or critical points of natural geometric quantities such as the length of a curve, the area of a surface or the energy of a map. For the corresponding variational problems it is often important to not only analyse the existence and properties of potential minimisers, but to obtain a more general understanding of the energy landscape. It is for example natural to ask whether an object that has energy very close to the minimal possible energy must also essentially "look like" a minimiser, and if so whether this holds in a quantitative sense, i.e. whether one can bound the distance to a minimiser in terms of the energy defect. Similarly one would like to understand whether points with small energy gradient must be close to a critical point and if so whether one can indeed bound the distance to the set of critical points by a power of the norm of the gradient. In this talk we will discuss some aspects of such quantitative estimates for geometric variational problems, such as for harmonic maps from surfaces, and their role in understanding the dynamics of the associated gradient flows.
01. Februar 2023, 17:15-19:00
Uhrturmhörsaal der Physik