Georgios Dimitroglou-Rizell

We combine techniques from symplectic topology and complex analysis to construct examples of rationally convex surfaces of genus g that are totally real outside of a number 2g-2 hyperbolic tangencies. We construct unknotted examples in the standard unit contact sphere in C2 that admit analytic fillings, as well as exact (and hence analytically non-fillable) knotted examples inside C2. This is joint work with Mark Lawrence.