Representation theory studies nonlinear algebraic structures by representing their elements as linear transformations of vector spaces. The interplay between homological and abstract categorical notions and concrete combinatorial structures is pivotal for studying representations of finite dimensional algebras. There has recently been fruitful interaction between this branch of representation theory and mathematical physics, algebraic combinatorics and topological data analysis, exemplified by the concepts cluster categories and of persistence modules, respectively.

In this project, experts from these fields will cooperate with representation theory specialist, aiming both for intrinsic progress in representation theory as well as concrete applications within these fields of application.