Topology of Electronic Phases

Condensed matter physics of many electron phases is the science that enabled (enables!) many of the  day-to-day "digital" technologies that we enjoy today. This subject has seen a revolution in the past ten years, with the concepts of topology and entanglement coming to the forefront. This talk will present an overview of these developments aimed at a broad audience. Starting from the elementary picture of the structure of a carbon atom, we will illustrate trivial and topological phases of electrons in one dimension. This will be followed by a description of our current understanding of all gapped phases of electrons, visiting the ten fold symmetry classification of fermionic systems via group cohomology. The talk will conclude with a brief description of open questions.