PhD defense: Topology, defects, and topological defects

The purpose of this Thesis is to theoretically investigate the power of topology on various problems in condensed-matter physics, as well as their possible applications for biological systems. This work was started in autumn 2016 in one world and is finishing in spring 2020, during the COVID-19 pandemic, in altered living conditions. One of the main ideas of this work is to show how the solution of certain problems may help in the most unexpected areas of not only physics but also science as a whole. This is exactly what society needs nowadays: fast graceful solutions. Topology like we show through the whole text might be one of those powerful tools to achieve them.