# Group of Dr. Alexander Stottmeister

We work on theoretical and mathematical aspects of quantum theory at the interface of quantum information theory and quantum field theory.

The main focus of our research is the development of a new approach to the renormalization group, called *operator algebraic renormalization,* in a quantum theoretical setting using mathematical tools from functional analysis and the theory of operator algebras.

Specific applications of this approach include rigorous constructions of models of quantum field theory as well as quantum simulation algorithms for quantum field theory, especially conformal field theory, with a priori error bounds.

To complement this research, we work on Bałaban’s approach to the renormalization group using classical probabilistic methods.

In addition, we are working on fundamental and mathematical concepts of quantum theory from an operator algebraic perspective, e.g., the Schmidt rank, embezzlement, and semi-group theory.

Our group is funded by the Stay Inspired Program of the MWK Lower Saxony.