Kolloquium Wilhelm Killing

Get an insight into the research of five 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.

• 1. Adrian Celestino ? Free probability, combinatorics and matrix models
• 2. Arghya Sadhukhan ? From lattices to flags: counting components via representation theory
• 3. Edoardo Tolotti ? Variational homogenization of the nonlinear Stokes problem
• 4. Beatriz Salvador ? From particle systems to PDEs and SPDEs
• 5. Anish Chedalavada ? TBA
• 6. Florian Riedel ? TBA
• 7. Mahdi Haghshenas ? TBA

I will present an overview of the results on existence and asymptotic properties of magnetic skyrmions defined as topologically nontrivial maps of degree +1 from the plane to a sphere which minimize a micromagnetic energy containing the exchange, perpendicular magnetic anisotropy and interfacial Dzyaloshinskii-Moriya interaction (DMI) terms. In ultrathin films, the stray field energy simply renormalizes the anisotropy constant at leading order, but in finite samples it also produces additional non-trivial contributions at the sample edges, promoting nontrivial spin textures. Starting with the whole space problem, I will first discuss the existence of single skyrmions as global energy minimizers at sufficiently small DMI strength. Then, using the quantitative rigidity of the harmonic maps I will present the asymptotic characterization of single skyrmion profiles both in infinite and finite samples. Lastly, I will touch upon the question of existence of multi-skyrmion solutions as minimizers with higher topological degree and present recent existence results obtained jointly with T. Simon and V. Slastikov.