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Introduction to Topological Phases of Matter

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I will talk a little about how we traditionally classify states of matter, and then blow this out of the water by introducing the idea of a topological phase of matter. The idea is that even fairly innocuous interactions between particles can result in striking collective behaviours at low energies; this includes sensitivity to the topology of the surface that the system is built on, and emergent “anyonic” particle-like objects, exhibiting properties that are impossible for fundamental particles in our universe. These phases of matter have connections to many areas of ongoing research, from pure mathematical classification problems, through dreams of quantum computation and quantum error correction, to condensed matter experiments. I will try to give a brief overview of how all this arises through simple examples.

This talk is part of the Trinity Mathematical Society series.

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