When topology meets strong interactions in quantum matter

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The study of strongly  interacting quantum matter has been at the forefront of condensed matter research in the last several decades. An independent development is the discovery of topological band insulators.  In this talk I will  describe phenomena that occur at the confluence of topology and strong interactions. I will first discuss  how insights from the study of the relatively simple topological insulators are revolutionizing our theoretical understanding of more complex quantum many body systems.  Next I will describe some experimental situations in which both band topology and strong correlations are present, the resulting novel phenomena, and the theoretical challenges they present.