Research Interests

Research Interests of Participants:

We are going to distribute a booklet with a description of each participant's research interests.  Please submit a short  description (less than one page) of your research interests below.

An example of research interests to submit can be found here: Sanders.tex. Please, email any questions to gearjuniorretreat@gmail.com. The paragraph that you need to submit should look as follows:

\section{Andrew Sanders (University of Illinois at Chicago)} \label{sanders}

My area of research is the the geometry, dynamics and analysis of 2 and 3-dimensional manifolds, particularly the study of geometric structures.  Much of my work thus far concerns the study of minimal surfaces in hyperbolic 3-manifolds; the central goal is to understand how the geometry of minimal surfaces influences the geometry of the ambient hyperbolic 3-manifold.

At this time, I am working on applying the ideas I have developed to the study of other geometric manifolds arising from representations of fundamental groups of surfaces into semisimple Lie groups (like $\mathrm{SL}(n,\mathbb{R})$ or $\mathrm{SL}(n,\mathbb{C})$). Spaces of such representations admit a parameterization coming from the complex analytic theory of Higgs bundles developed by Hitchin.  The study of equivariant minimal surfaces has a natural interpretation in terms of Higgs bundles, and I am hoping to use this relationship to better understand certain aspects of the non-abelian Hodge correspondence.

Thursday, May 22, 2014

Organizers

Dick Canary

Steve Kerckhoff

Michelle Lee

Ben Linowitz

Sara Maloni

Laura Schaposnik

Anna Wienhard

GEAR Executive Committee

William Goldman

Steve Kerckhoff

Richard Wentworth

Anna Wienhard

Contact information