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I won’t actually discuss quantum groups, but rather the representation theoretic foils of “finite” quantum groups called modular tensor categories (MTCs). The simplest example of a MTC is the Drinfeld center DG-Rep of a representation category G-Rep, where G is a finite group. When studying MTCs, one might ask if it’s possible to remove the non-quantum part. It turns out there is, via a process called "taking the core" of an MTC. There is also a kind of inverse process called gauging. I won’t get into too many gory categorical details, because I’m really just interested in the (2+1)-dimensional topological quantum field theories (TQFTs) they encode. In particular, it appears that such a TQFT is universal for topological quantum computing if and only if the TQFT corresponding to its core is. I’ll discuss all of this in more detail and sketch a possible proof using the Birman-Hilden theorem.

This is a continuation of my previous talk.