Enhancing user-centred educational design: Developing personas of mathematics school students.

Persona development techniques are a well-established method to create relatable descriptions of representatives of target users of digital systems. In the field of education, research on learner characteristics has yielded comprehensive results that can help advance educational approaches. Nonetheless, these results often remain abstract and distant for researchers and practitioners.

Doubling of Asymptotically Flat Half-spaces and the Riemannian Penrose Inequality.

Building on previous works of Bray, of Miao, and of Almaraz, Barbosa, and de Lima, we develop a doubling procedure for asymptotically flat half-spaces (, ) with horizon boundary and mass . If , (, ) has non-negative scalar curvature, and the boundary is mean-convex, we obtain the Riemannian Penrose-type inequality as a corollary. Moreover, in the case where is not totally geodesic, we show how to construct local perturbations of (, ) that increase the scalar curvature.

The Willmore Center of Mass of Initial Data Sets.

We refine the Lyapunov-Schmidt analysis from our recent paper (Eichmair and Koerber in Large area-constrained Willmore surfaces in asymptotically Schwarzschild 3-manifolds. arXiv preprint arXiv:2101.12665, 2021) to study the geometric center of mass of the asymptotic foliation by area-constrained Willmore surfaces of initial data for the Einstein field equations.

Initial Data Rigidity Results.

We prove several rigidity results related to the spacetime positive mass theorem. A key step is to show that certain marginally outer trapped surfaces are weakly outermost. As a special case, our results include a rigidity result for Riemannian manifolds with a lower bound on their scalar curvature.