Topology as a branch of mathematics studies the properties of the objects that remain conserved under the continuous deformations. However, despite its abstact nature topology is directly related to physics providing an explanation of precise quantization of Hall resistance in quantum Hall effect which takes place even in the presence of defects, the phenomenon of anomalous velocity and the range of other phenomena. The importance of discovery of topological phases of matter and topological phase transitions has been marked by 2016 Nobel Prize in Physics.
Topological photonics investigates the possibilities to realize the topological states of light protected from scattering on defects and imperfections of the structure and promising the next generation of devices for all-optical signal processing protected from the disorder. Our group at ITMO studies the topological states of classical and quantum light developing both fundamental and applied concepts.