Gromov-Thurston manifolds are a class of manifolds that admit negatively curved metrics, but no locally symmetric metric. They are one of the few known examples of such manifolds, although there is reason to expect that there are many such manifolds. If we want to understand such manifolds in general, a thorough understanding of Gromov-Thurston manifolds, including a classification in some reasonable sense, is a good starting point. However, due to their non-symmetric nature, computations and even estimates of any geometric invariant prove exceedingly difficult. In this talk, we present some ongoing work about a system of equations that allows us to compute the entropy of Gromov-Thurston manifolds. If there is time, we discuss how this can help us towards a classification.

The first 45 minutes will cover the construction of Gromov-Thurston manifolds and the definition of entropy, including ways to compute it. The second 45 minutes will be about the ongoing work.