Learning Seminar in Algebraic Combinatorics: Tropical linear spaces and tropical Grassmannians

Matroids are hard. Valuated matroids generalize matroids. Tropical linear spaces are equivalent to valuated matroids. Therefore, tropical linear spaces are hard, so are their parameter spaces: the Dressians, the tropical analog of the Grassmannians. Inside the Dressian there is a nicer subset, called the tropical Grassmannian, that parametrizes the tropicalized linear spaces. I will familiarize the audience with these concepts with a lot of examples.