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Congrats to our new Doctors rer. nat. (01.12.2022)
Once again, we are happy to announce that three of our students have taken the big career step and successfully defended their PhD theses. Congratulations to Chiara Meroni, Henrik Eisenmann, and Daniel Schliewe!
Henrik Eisenmann successfully defended his PhD thesis "Multilinear optimization in low-rank models" on October 13, 2022, at the University of Leipzig.
In his thesis, he studied three different topics revolving around tensors of low rank. Tensors play an important role in many applications and are fundamental objects of multilinear algebra and multivariate functions. When handling partial differential equations, the solutions often lie in the closure of a tensor space. In several fields of research, for example, in psychometrics, chemometrics, recommendation systems, and signal processing, data appears in the form of multidimensional arrays. Multilinear maps and homogeneous polynomials are naturally identified as tensors and symmetric tensors, respectively.
Henrik has already started a postdoctoral job at RWTH Aachen, where he now researches parametric partial differential equations and hopes to learn about new topics in mathematics. He studied Mathematics at TU Berlin. At our institute, he was a PhD student under the supervision of André Uschmajew.
Chiara Meroni successfully defended her PhD thesis, "Semialgebraische konvexe Körper" on October 25, 2022, at the University of Leipzig.
Her thesis focuses on some geometrical objects, called semialgebraic convex bodies, that classically have been studied from a mostly analytical point of view. In her thesis, she tried (with the help of many amazing collaborators) to study classical problems in convex geometry from the point of view of algebraic geometry instead. The results of this approach show how powerful it is to look at the same thing from different points of view, and the different approaches together bring new insight into old and new questions.
Chiara comes from Italy and studied for her bachelor and master in Trieste. She came to Leipzig for a summer school and loved it, so she decided to apply for a PhD position at our institute. She was supervised by Bernd Sturmfels and Rainer Sinn, which made these two years very interesting and exciting for her. Chiara is still working at our MPI. In February, she will move to ICERM Institute for Computational and Experimental Research in Mathematics in Providence, USA, for a postdoc position.
Daniel Schliewe successfully defended his PhD thesis, "BPX-Type Preconditioners and Convergence Estimates for Strictly Quasiconvex Functionals" on November 2 at the University of Leipzig.
Daniel obtained a significant result in the rigorous numerical analysis of nonlinear elasticity. He showed that strict quasi-convexity, which is a substantial weakening of strict convexity and the right notion for elasticity, is sufficient to reliably benefit from a multi-grid approach. Indeed, generic local strict convexity in a weak topology upgrades to strict convexity in the energy topology.