Topology meets quantum mechanics

When abstract mathematical concepts find meaning in physical phenomena, revolutionary new theories of physics are often invented. such as the theories of general relativity and quantum mechanics. In the past few decades, a revolution has happened in our understanding of matter that was caused by the combination of quantum mechanics and the theory of topology. It has been discovered that when matter is topological, twists in their wave function bring up exotic properties, which might also have applications for the next generation of electronics. In this talk, I will review basic concepts and the development of the topological understanding of matter.