In our third tutorial we continue to sketch the deformation theory of Riemann surfaces by means of goodwill and example, and lots of pictures. Our examples illustrate that algebraic objects can be geometric, and geometric objects can be number theoretic! We pursue some surprisingly beautiful low-hanging fruit of these correspondences (and point to some staggering summits) which we consider collectively as "Jabberwocky." --- The notion of Jabberwocky is anecdotal of course, but in a sense described by David Blackwell, apropos of our meeting here at PUNDiT! Ultimately, we understand the parametrization spaces of geometric structures on Riemann surfaces as being contained in certain algebro-geometric-analytic objects known as character varieties. Our examples culminate with a demonstration of the relationship of the Standard Markov equation with the behavior of simple closed geodesics on a maximally symmetric once punctured torus. culminate with a demonstration of the relationship of the Standard Markov equation with the behavior of simple closed geodesics on a maximally symmetric once punctured torus.
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