One of the central fundamental topics of modern science is the question of emergence of complex dynamics. Existing theory can understand the emergence of complex dynamics from the microscopic quantum laws in only very limited cases. The project is based on unconventional algebraic principles discovered by the principal investigator (PI) called “dynamical symmetries”, which have potentially broad applications ranging from operator algebras, through novel passive quantum error correcting algorithms in realistic quantum computing platforms to computing complex dynamics in driven quantum matter experiments. During the internship, we will focus on lattice models, e.g., spin models. For example, one part of the project could be discovering new models that display complex dynamics like a 2D version of the “spin lace model” with quantum many-body scars. A more mathematically oriented student will benefit from studying the stability of the resulting scarred phases using methods similar to the “scarring phase transition” stability analysis. However, these are merely examples and interested and highly motivated candidates should contact the PI to discuss the project details.