### University of Arkansas Topology Seminar: 11/16/2017

### Speaker: Neil Hoffman

### Title: Unifying unexpected lens space surgeries

The Berge Conjecture attempts to classify knots in *S*^{3} which admit a (non-trivial) lens space surgery. After providing some background for this problem, we will discuss why the natural generalization of this conjecture to knots in lens spaces which admit a second lens space surgery fails. Following this discussion, we will see how to make some sense of these counter-examples. This is joint work with Ken Baker, Nathan Dunfield, and Joan Licata.

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