Eric Rowell (Texas A&M): Mathematical Problems in Topological Quantum Computation

Two-dimensional topological states of matter offer a route to quantum computation that would be topologically protected against the nemesis of the quantum circuit model: decoherence.  In this talk I will give a mathematicians’ perspective on some of the advantages and challenges of this model, focusing on the interplay of condensed matter physics, representation theory, low-dimensional topology and category theory.  We will discover some compelling mathematical questions inspired by foundational problems in topological information theory along the way, and I will present a few results and ongoing projects with collaborators.