One of the greatest triumphs of the 20th century was development of quantum theory solids, which allowed us to understand why some materials are electrically insulating whereas others are conductors. To the surprise of all physicists, we now know that there is a new class of materials, known as topological insulators, that likes to be both. Topological insulators are expected to have an insulating bulk and topologically protected surface states, with many unique properties. Professor Kurdak will expose some of the beautiful features of this unexpected state of matter, using examples from a broad range of recent experiments including from his own research on samarium hexaboride.