Juan was a PhD student in our group at CASUS from 2020 to 2025. His research combined numerical analysis and machine learning, with a particular focus on introducing Sobolev cubatures to discretize Sobolev gradient flows in variational problems. This approach helps mitigate numerical stiffness, which is especially relevant in applications such as autoencoders and PINNs and autoencoders and PDEs with jump discontinuities. 

After completing his PhD in collaboration with TU Dresden, Juan continued his research at the Max Planck Institute CBG and is now a postdoctoral researcher at the Bavarian AI Chair for Mathematical Foundations of Artificial Intelligence at Ludwig-Maximilians-Universität München, led by Prof. Gitta Kutyniok.

Gentian was a PhD student in our group at CASUS from 2021 to 2025. Gentian Zavalani is a researcher specializing in numerical analysis, with a focus on solving partial differential equations and performing numerical integration on complex geometries, particularly smooth surfaces. His work combines numerical methods with differential geometry to develop accurate and efficient algorithms for geometric computations, such as curvature estimation and high-order surface integration. Key contributions include global polynomial level set parametrizations, high-order integration techniques on triangulated surfaces, and error analysis of numerical schemes. He is currently a member of Prof. Oliver Sander's chair of Numerical Methods of Partial Differentiual Equations, Technical University Dresden (TUD).