MSCA Individual Fellowship for Tropical Methods in Mathematics and Computer Science

Dr. Oliver Lorscheid received an MSCA Individual Fellowship for his interdisciplinary research on "Tropical Methods in Mathematics and Computer Science." This project covers topics in tropical geometry that range from its foundations to concrete applications, and is pursued in collaboration with other mathematicians and computer scientists. The main objectives are the following.

(1) Tropical arithmetic allows for new algorithmic techniques to solve mean payoff games. We follow this path to develop fast algorithms and to tackle the 'P versus NP'-problem in this context.

(2) Based on our previous construction of moduli spaces of matroids, we have developed a novel method to study representations of matroids. Through this new lense, we are able to extend previous results and to unearth yet hidden laws.

(3) A cohomological explanation of the tropical Riemann-Roch theorem might be called the philosopher's stone of tropical scheme theory. The times are ripe to embark on this quest.