Mathematics Münster

Get an insight into the research of seven new postdoctoral researchers of Mathematics Münster. In short scientific presentations they will introduce their topics.
After the talks, there will be the opportunity to exchange ideas while enjoying tea, coffee and cake in the Common Room.

Abstract

Due to its catastrophic character, brittle fracture has been an important object of investigation in fracture mechanics. The idea of a fracture energy proportional to the measure of the fracture surface is due to Griffith. The revisitation of the subject by Francfort and Marigo offered a genuinely variational formulation of the problem.
For the mathematical community, the interest in fracture problems originated from its reformulation as a free discontinuity problem (FDP), following the approach by De Giorgi and Ambrosio to analyze the Mumford and Shah image segmentation functional.
After introducing the mathematical setting for FDPs, I will survey on several basic problems to allow the use of variational methods to establish existence of weak/strong minimizers and their phase-field approximation, both for Griffith type energies and for cohesive fracture models. The latter have been the subject of much attention recently and are based on FDPs with surface densities that are concave and bounded functions of the jump amplitude.

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We invite all early career researchers who have started their position at Mathematics Münster in 2025 to join us for this MM Welcome Event. Learn more about the Cluster, its research topics and opportunities. Get to know investigators and your fellow new colleagues.

tba

The Anti-de-Sitter (AdS) space is the analogue in Lorentzian geometry to the hyperbolic space of negative constant curvature familiar to Riemannian geometers. The study of the Anti-de-Sitter space and more generally, of solutions to the Einstein equations which ressemble the Anti-de-Sitter space has many applications in high energy physics and provides mathematicians with problems lying at the intersection of Lorenzian geometry and hyperbolic pdes. I will start with a general introduction to the study of the Einstein equations, with an emphasis on the evolution problem. I will then briefly discuss the well-posedness for wave equations, including the Einstein equations, in the case of AdS type boundaries. In the second part of the talk, I will present several results concerning the linear or non-linear perturbations of the AdS space for the vacuum Einstein equations and some related toy models.