Collection Combinatorial Algebra up to Symmetry
Mathematical objects in combinatorial algebra often have rich algebraic, combinatorial and geometric structures. For example, this can be reﬂected in large symmetry groups which is the main focus of these lectures. Such phenomena had recently applications in various related areas like algebraic statistics or representation theory. We discuss relevant foundations, recent results and open questions especially on the asymptotic behavior of algebraic, combinatorial and geometric properties of sequences of symmetric objects of interest.