With polytopes to an excellent dissertation

Marie-Charlotte Brandenburg successfully completed her doctorate on the “Tropical Positivity and Semialgebraic Sets from Polytopes”. She will remain at the MPI as a postdoc in the Math Machine Learning Group. Heartfelt congratulations!

Marie-Charlotte's dissertation focuses on polytopes, which are fundamental objects in geometry and mathematics as a whole. Dating back to Plato and Archimedes, it may come as a surprise that they still prove to be rich objects of study to this day. Yet even now, they continue to appear in new mathematical contexts. In her thesis, she explores questions from optimization, geometric tomography, and game theory.

One example of such a question is to describe the tropicalization of matrices with positive entries and bounded rank, or to classify the combinatorial types of polytopes that arise as the set of correlated equilibria in game theory. To address these questions, she studies the interplay between polyhedral structures and semi-algebraic sets, building the bridge between discrete and (real) algebraic geometry using tropical methods.

Marie-Charlotte Brandenburg earned her bachelor's and master's degrees in mathematics at the Free University of Berlin. She commenced her first year as a PhD student with Rainer Sinn in Berlin and moved to Leipzig in 2020, since her advisor now works at the Mathematical Institute of Leipzig University. Marie-Charlotte recently joined Guido Montufar's group on Mathematical Machine Learning, which is part of the SPP Theoretical Foundations of Deep Learning. In her postdoctoral position she wants to investigate the connection between tropical geometry and ReLU Neural Networks.