Israeli-German WE-Heraeus-Seminar — Unifying Aspects of Topology in Quantum and Classical Systems

In topology, properties of a geometric object are identified which remain unchanged under continuous deformations. Those properties are then referred to as topological invariants. This mathematical concept gains ever more importance in many branches of physics, comprising general relativity, quantum field theory, quantum chromodynamics, condensed matter, strongly correlated many-body system, magnetism, soft matter physics, and symmetry classification issues. Topological phases of matter have emerged as a far-reaching scientific breakthrough in the 21st century. The topological states were initially conceived as exotic states that are labeled by topological invariants interpreted as quantum numbers. Furthermore, the exotic transport properties exhibited by topological materials have been harnessed for applications in quantum technologies, making topology a very active research topic in quantum information theory and quantum computing. More recently, topological concepts have been studied in an increasingly diverse list of disciplines, also including applications in classical physics such as mechanics of elastic and deformable bodies, nonlinear dynamics, and biophysics. There are also considerable activites in mathematical physics.