Wolf, Michael2017-08-032017-08-032016-052016-04-20May 2016Acosta, Jorge A.. "Holonomy Limits of Cyclic Opers." (2016) Diss., Rice University. <a href="https://hdl.handle.net/1911/96525">https://hdl.handle.net/1911/96525</a>.https://hdl.handle.net/1911/96525Given a Riemann surface $X = (\Sigma, J)$, we find an expression for the dominant term for the asymptotics of the holonomy of opers over that Riemann surface corresponding to rays in the Hitchin base of the form $(0,0,\cdots,t\omega_n)$. Moreover, we find an associated equivariant map from the universal cover $(\tilde{\Sigma},\tilde{J})$ to the symmetric space SL$_n(\mathbb{C}) / \mbox{SU}(n)$ and show that limits of these maps tend to a sub-building in the asymptotic cone. That sub-building is explicitly constructed from the local data of $\omega_n$.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.RepresentationsAsymptoticsDifferential EquationsThesis2017-08-03