Personal webpage - Otto T.P. Schmidt

Hey, this is my landing page for academic purposes.

My name is Otto, and I am a physicist working on mathematical aspects of quantum condensed matter physics. In my PhD, which I am pursuing as part of the Marie Skłodowska-Curie PhD Fellowship TENORS, I apply methods from algebraic geometry to problems in quantum many-body physics.

A central object of my research are tensor networks in various forms. These networks are powerful tools for gaining both numerical and conceptual insights into complex quantum systems and have become increasingly popular in recent years. Mathematically, tensor networks can be viewed as rational maps from a parameter space to an embedding space. Since these maps are polynomial, they define irreducible varieties in the embedding space cut out by the Zariski closure of the image. That is nice since it allows to look at physical system in a algebraic way.

Studying tensor networks through this algebro-geometric lens raises the level of abstraction and can lead to new insights into how these networks represent physical systems. What can we understand about the physical state by looking at geometric properties like the degree of dimension of the variety?