Geometry and Topology in Condensed Matter Physics
Research Collaboration at the University of Greifswald
About us
In recent years, a vibrant research community has developed at the University of Greifswald at the intersection of mathematics and physics. Our shared focus lies on geometric and topological structures in physical systems—from condensed matter to astrophysical phenomena.
Research Areas
Topological Phases of Matter
Topological properties of physical systems have led to a fundamental understanding of new material classes in recent decades. Our research examines how topological invariants persist even in realistic, disordered, or interacting systems and what experimental signatures arise from this. This includes work on topological insulators, superconductors, and magnetic textures such as skyrmions.
Quantum Geometry and Berry Phases
Geometric structures in the parameter space of quantum mechanical Hamiltonians play a central role in transport phenomena, symmetry breaking, and phase transitions. We develop theoretical frameworks to characterize these geometric invariants and understand their experimental relevance in strongly correlated systems, superconductivity, and spintronics.
Geometry in Curved Spacetimes
The application of geometric and topological methods to relativistic systems opens new perspectives for understanding turbulence in astrophysical environments, black hole dynamics, and analytic index theorems on Lorentzian manifolds. These works combine mathematical rigor with concrete astrophysical questions.
Participating Researchers
Saikat Banerjee – Theoretical Physics, Strong Correlations, Topological Materials
Alexander Engel – Mathematics, Coarse Geometry
Matthias Eschrig – Theoretical Physics, Condensed Matter Physics
Ines Kath – Mathematics, Pseudo-Riemannian Differential Geometry
Matthias Ludewig – Mathematics, Non-Commutative Geometry
Markus Münzenberg – Experimental Physics, Interface and Surface Physics
Anna Posazhennikova – Theoretical Physics, Condensed Matter Physics, Cold Atoms
Nima Rasekh – Mathematics, Homotopy Theory
Daniel Siegel – Theoretical Physics, Plasma Astrophysics
Konrad Waldorf – Mathematics, Geometry & Topology